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arxiv-677301 | quant-ph/0502009 | Quantum Information Theoretical Analysis of Various Constructions for Quantum Secret Sharing | <|reference_start|>Quantum Information Theoretical Analysis of Various Constructions for Quantum Secret Sharing: Recently, an information theoretical model for Quantum Secret Sharing (QSS) schemes was introduced. By using this model, we prove that pure state Quantum Threshold Schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the Monotone Span Program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation.<|reference_end|> | arxiv | @article{rietjens2005quantum,
title={Quantum Information Theoretical Analysis of Various Constructions for
Quantum Secret Sharing},
author={Karin Rietjens, Berry Schoenmakers, Pim Tuyls},
journal={arXiv preprint arXiv:quant-ph/0502009},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0502009},
primaryClass={quant-ph cs.CR}
} | rietjens2005quantum |
arxiv-677302 | quant-ph/0502031 | Mutually Unbiased Bases are Complex Projective 2-Designs | <|reference_start|>Mutually Unbiased Bases are Complex Projective 2-Designs: Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is unknown whether this bound can be achieved for any non-prime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0,1/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2-designs with angle set {1/(d+1)}.<|reference_end|> | arxiv | @article{klappenecker2005mutually,
title={Mutually Unbiased Bases are Complex Projective 2-Designs},
author={Andreas Klappenecker (Texas A&M University) and Martin Roetteler (NEC
Laboratories America, Inc.)},
journal={Proceedings 2005 IEEE International Symposium on Information
Theory (ISIT 2005), Adelaide, Australia, pp. 1740-1744, 2005},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0502031},
primaryClass={quant-ph cs.ET}
} | klappenecker2005mutually |
arxiv-677303 | quant-ph/0502072 | NP-complete Problems and Physical Reality | <|reference_start|>NP-complete Problems and Physical Reality: Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and "anthropic computing." The section on soap bubbles even includes some "experimental" results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.<|reference_end|> | arxiv | @article{aaronson2005np-complete,
title={NP-complete Problems and Physical Reality},
author={Scott Aaronson},
journal={ACM SIGACT News, March 2005},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0502072},
primaryClass={quant-ph cs.CC gr-qc}
} | aaronson2005np-complete |
arxiv-677304 | quant-ph/0502101 | Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors | <|reference_start|>Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors: We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components -- such as single photon sources, beam splitters and phase shifters -- are perfect and introduce no errors. We make use of the fact that the error model induced by the lossy hardware is that of an erasure channel, i.e., the error locations are always known. Using a method based on a Markov chain description of the error correction procedure, our calculations show that, with the 7 qubit CSS quantum code, the gate error threshold for fault tolerant quantum computation is bounded below by a value between 1.78% and 11.5% depending on the construction of the entangling gates.<|reference_end|> | arxiv | @article{silva2005thresholds,
title={Thresholds for Linear Optics Quantum Computing with Photon Loss at the
Detectors},
author={Marcus Silva, Martin Roetteler, Christof Zalka},
journal={Phys. Rev. A 72, 032307 (2005)},
year={2005},
doi={10.1103/PhysRevA.72.032307},
archivePrefix={arXiv},
eprint={quant-ph/0502101},
primaryClass={quant-ph cs.ET}
} | silva2005thresholds |
arxiv-677305 | quant-ph/0502138 | New Tales of the Mean King | <|reference_start|>New Tales of the Mean King: The Mean King's problem asks to determine the outcome of a measurement that is randomly selected from a set of complementary observables. We review this problem and offer a combinatorial solution. More generally, we show that whenever an affine resolvable design exists, then a state reconstruction problem similar to the Mean King's problem can be defined and solved. As an application of this general framework we consider a problem involving three qubits in which the outcome of nine different measurements can be determined without using ancillary qubits. The solution is based on a measurement derived from Hadamard designs.<|reference_end|> | arxiv | @article{klappenecker2005new,
title={New Tales of the Mean King},
author={Andreas Klappenecker (Texas A&M University) and Martin Roetteler (NEC
Laboratories America, Inc.)},
journal={arXiv preprint arXiv:quant-ph/0502138},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0502138},
primaryClass={quant-ph cs.ET}
} | klappenecker2005new |
arxiv-677306 | quant-ph/0502185 | Quantum Implementation of Parrondo's Paradox | <|reference_start|>Quantum Implementation of Parrondo's Paradox: We propose a quantum implementation of a capital-dependent Parrondo's paradox that uses $O(\log_2(n))$ qubits, where $n$ is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.<|reference_end|> | arxiv | @article{miszczak2005quantum,
title={Quantum Implementation of Parrondo's Paradox},
author={J. A. Miszczak, P. Gawron},
journal={Fluctuation and Noise Letters, Vol. 5, No. 4 (2005)},
year={2005},
doi={10.1142/S0219477505002902},
archivePrefix={arXiv},
eprint={quant-ph/0502185},
primaryClass={quant-ph cs.GT}
} | miszczak2005quantum |
arxiv-677307 | quant-ph/0503027 | A Three-Stage Quantum Cryptography Protocol | <|reference_start|>A Three-Stage Quantum Cryptography Protocol: We present a three-stage quantum cryptographic protocol guaranteeing security in which each party uses its own secret key. Unlike the BB84 protocol, where the qubits are transmitted in only one direction and classical information exchanged thereafter, the communication in the proposed protocol remains quantum in each stage. A related system of key distribution is also described.<|reference_end|> | arxiv | @article{kak2005a,
title={A Three-Stage Quantum Cryptography Protocol},
author={Subhash Kak},
journal={Foundations of Physics Letters 19 (2006), 293-296.},
year={2005},
doi={10.1007/s10702-006-0520-9},
archivePrefix={arXiv},
eprint={quant-ph/0503027},
primaryClass={quant-ph cs.CR}
} | kak2005a |
arxiv-677308 | quant-ph/0503114 | On the Power of Random Bases in Fourier Sampling: Hidden Subgroup Problem in the Heisenberg Group | <|reference_start|>On the Power of Random Bases in Fourier Sampling: Hidden Subgroup Problem in the Heisenberg Group: The hidden subgroup problem (HSP) provides a unified framework to study problems of group-theoretical nature in quantum computing such as order finding and the discrete logarithm problem. While it is known that Fourier sampling provides an efficient solution in the abelian case, not much is known for general non-abelian groups. Recently, some authors raised the question as to whether post-processing the Fourier spectrum by measuring in a random orthonormal basis helps for solving the HSP. Several negative results on the shortcomings of this random strong method are known. In this paper however, we show that the random strong method can be quite powerful under certain conditions on the group G. We define a parameter r(G) for a group G and show that O((\log |G| / r(G))^2) iterations of the random strong method give enough classical information to identify a hidden subgroup in G. We illustrate the power of the random strong method via a concrete example of the HSP over finite Heisenberg groups. We show that r(G) = \Omega(1) for these groups; hence the HSP can be solved using polynomially many random strong Fourier samplings followed by a possibly exponential classical post-processing without further queries. The quantum part of our algorithm consists of a polynomial computation followed by measuring in a random orthonormal basis. This gives the first example of a group where random representation bases do help in solving the HSP and for which no explicit representation bases are known that solve the problem with (\log G)^O(1) Fourier samplings. As an interesting by-product of our work, we get an algorithm for solving the state identification problem for a set of nearly orthogonal pure quantum states.<|reference_end|> | arxiv | @article{radhakrishnan2005on,
title={On the Power of Random Bases in Fourier Sampling: Hidden Subgroup
Problem in the Heisenberg Group},
author={Jaikumar Radhakrishnan, Martin Roetteler, and Pranab Sen},
journal={Proceedings 32nd International Conference on Automata, Languages,
and Programming (ICALP 2005), Lisbon, Portugal, Springer LNCS, pp. 1399-1411,
2005},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0503114},
primaryClass={quant-ph cs.ET}
} | radhakrishnan2005on |
arxiv-677309 | quant-ph/0503139 | Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes | <|reference_start|>Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes: It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors with fidelity exponentially close to 1, at the price of increasing the size of the registers (i.e., the coding alphabet). This demonstrates a sharp distinction between exact and approximate quantum error correction. The codes have the property that any $t$ components reveal no information about the message, and so they can also be viewed as error-tolerant secret sharing schemes. The construction has several interesting implications for cryptography and quantum information theory. First, it suggests that secret sharing is a better classical analogue to quantum error correction than is classical error correction. Second, it highlights an error in a purported proof that verifiable quantum secret sharing (VQSS) is impossible when the number of cheaters t is n/4. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model.<|reference_end|> | arxiv | @article{crepeau2005approximate,
title={Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes},
author={Claude Crepeau and Daniel Gottesman and Adam Smith},
journal={Preliminary version in proceedings of "Advances in Cryptology --
EUROCRYPT 2005"},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0503139},
primaryClass={quant-ph cs.CR}
} | crepeau2005approximate |
arxiv-677310 | quant-ph/0503157 | Secure Communication Using Qubits | <|reference_start|>Secure Communication Using Qubits: A two-layer quantum protocol for secure transmission of data using qubits is presented. The protocol is an improvement over the BB84 QKD protocol. BB84, in conjunction with the one-time pad algorithm, has been shown to be unconditionally secure. However it suffers from two drawbacks: (1) Its security relies on the assumption that Alice's qubit source is perfect in the sense that it does not inadvertently emit multiple copies of the same qubit. A multi-qubit emission attack can be launched if this assumption is violated. (2) BB84 cannot transfer predetermined keys; the keys it can distribute are generated in the process. Our protocol does not have these drawbacks. As in BB84, our protocol requires an authenticated public channel so as to detect an intruder's interaction with the quantum channel, but unlike in symmetric-key cryptography, the confidentiality of transmitted data does not rely on a shared secret key.<|reference_end|> | arxiv | @article{hosseini-khayat2005secure,
title={Secure Communication Using Qubits},
author={Saied Hosseini-Khayat, Iman Marvian},
journal={The Sixth IEEE International Conference on Computer and
Information Technology, 2006. Seoul, South Korea},
year={2005},
doi={10.1109/CIT.2006.164},
archivePrefix={arXiv},
eprint={quant-ph/0503157},
primaryClass={quant-ph cs.CR}
} | hosseini-khayat2005secure |
arxiv-677311 | quant-ph/0503230 | Programmable Quantum Networks with Pure States | <|reference_start|>Programmable Quantum Networks with Pure States: Modern classical computing devices, except of simplest calculators, have von Neumann architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in quantum computing, communications and control. It is also interesting for the modern theoretical research in the quantum information science and raises challenging questions about an experimental assessment of such a programmable models. Together with some progress in the given direction, such ideas encounter specific problems arising from the very essence of quantum laws. Currently are known two different ways to overcome such problems, sometime denoted as a stochastic and deterministic approach. The presented paper is devoted to the second one, that is also may be called the programmable quantum networks with pure states. In the paper are discussed basic principles and theoretical models that can be used for the design of such nano-devices, e.g., the conditional quantum dynamics, the Nielsen-Chuang "no-programming theorem, the idea of deterministic and stochastic quantum gates arrays. Both programmable quantum networks with finite registers and hybrid models with continuous quantum variables are considered. As a basic model for the universal programmable quantum network with pure states and finite program register is chosen a "Control-Shift" quantum processor architecture with three buses introduced in earlier works. It is shown also, that quantum cellular automata approach to the construction of an universal programmable quantum computer often may be considered as the particular case of such design.<|reference_end|> | arxiv | @article{vlasov2005programmable,
title={Programmable Quantum Networks with Pure States},
author={Alexander Yu. Vlasov},
journal={arXiv preprint arXiv:quant-ph/0503230},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0503230},
primaryClass={quant-ph cs.OH}
} | vlasov2005programmable |
arxiv-677312 | quant-ph/0503236 | On Self-Dual Quantum Codes, Graphs, and Boolean Functions | <|reference_start|>On Self-Dual Quantum Codes, Graphs, and Boolean Functions: A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regular graphs having minimum regular vertex degree and containing long cycles. Two graphs correspond to equivalent quantum codes if they are related by a sequence of local complementations. We use this operation to generate orbits of graphs, and thus classify all inequivalent self-dual additive codes over GF(4) of length up to 12, where previously only all codes of length up to 9 were known. We show that these codes can be interpreted as quadratic Boolean functions, and we define non-quadratic quantum codes, corresponding to Boolean functions of higher degree. We look at various cryptographic properties of Boolean functions, in particular the propagation criteria. The new aperiodic propagation criterion (APC) and the APC distance are then defined. We show that the distance of a zero-dimensional quantum code is equal to the APC distance of the corresponding Boolean function. Orbits of Boolean functions with respect to the {I,H,N}^n transform set are generated. We also study the peak-to-average power ratio with respect to the {I,H,N}^n transform set (PAR_IHN), and prove that PAR_IHN of a quadratic Boolean function is related to the size of the maximum independent set over the corresponding orbit of graphs. A construction technique for non-quadratic Boolean functions with low PAR_IHN is proposed. It is finally shown that both PAR_IHN and APC distance can be interpreted as partial entanglement measures.<|reference_end|> | arxiv | @article{danielsen2005on,
title={On Self-Dual Quantum Codes, Graphs, and Boolean Functions},
author={Lars Eirik Danielsen (University of Bergen)},
journal={arXiv preprint arXiv:quant-ph/0503236},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0503236},
primaryClass={quant-ph cs.IT math.IT}
} | danielsen2005on |
arxiv-677313 | quant-ph/0503238 | Optimization of Partial Search | <|reference_start|>Optimization of Partial Search: Quantum Grover search algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster, this is partial search. A partial search algorithm was recently suggested by Grover and Radhakrishnan. Here we optimize it. Efficiency of the search algorithm is measured by number of queries to the oracle. The author suggests new version of Grover-Radhakrishnan algorithm which uses minimal number of queries to the oracle. The algorithm can run on the same hardware which is used for the usual Grover algorithm.<|reference_end|> | arxiv | @article{korepin2005optimization,
title={Optimization of Partial Search},
author={Vladimir Korepin},
journal={Journal of Physics A: Math. Gen. vol 38, pages L731-L738, 2005},
year={2005},
doi={10.1088/0305-4470/38/44/L02},
number={YITP-SB-05-08},
archivePrefix={arXiv},
eprint={quant-ph/0503238},
primaryClass={quant-ph cs.DS}
} | korepin2005optimization |
arxiv-677314 | quant-ph/0503239 | On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States | <|reference_start|>On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States: We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in $\C^n$ which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.<|reference_end|> | arxiv | @article{klappenecker2005on,
title={On Approximately Symmetric Informationally Complete Positive
Operator-Valued Measures and Related Systems of Quantum States},
author={Andreas Klappenecker, Martin Roetteler, Igor Shparlinski, Arne
Winterhof},
journal={Journal of Mathematical Physics, 46:082104, 2005},
year={2005},
doi={10.1063/1.1998831},
archivePrefix={arXiv},
eprint={quant-ph/0503239},
primaryClass={quant-ph cs.ET}
} | klappenecker2005on |
arxiv-677315 | quant-ph/0504007 | Probabilistic Model--Checking of Quantum Protocols | <|reference_start|>Probabilistic Model--Checking of Quantum Protocols: We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.<|reference_end|> | arxiv | @article{gay2005probabilistic,
title={Probabilistic Model--Checking of Quantum Protocols},
author={Simon Gay, Rajagopal Nagarajan, Nikolaos Papanikolaou},
journal={arXiv preprint arXiv:quant-ph/0504007},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0504007},
primaryClass={quant-ph cs.LO}
} | gay2005probabilistic |
arxiv-677316 | quant-ph/0504012 | Quantum search algorithms | <|reference_start|>Quantum search algorithms: We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on quantum walks.<|reference_end|> | arxiv | @article{ambainis2005quantum,
title={Quantum search algorithms},
author={Andris Ambainis},
journal={SIGACT News, 35 (2):22-35, 2004.},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0504012},
primaryClass={quant-ph cs.CC cs.DS}
} | ambainis2005quantum |
arxiv-677317 | quant-ph/0504021 | Numerical Simulations of a Possible Hypercomputational Quantum Algorithm | <|reference_start|>Numerical Simulations of a Possible Hypercomputational Quantum Algorithm: The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, Hilbert's tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.<|reference_end|> | arxiv | @article{sicard2005numerical,
title={Numerical Simulations of a Possible Hypercomputational Quantum Algorithm},
author={Andr'es Sicard, Juan Ospina, Mario V'elez},
journal={In "Adaptive and Natural Computing Algorithms. Proc. of the
International Conference in Coimbra, Portugal". Bernardete Ribeiro et al.
(eds.). SpringerWienNewYork, 2005. p. 272--275},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0504021},
primaryClass={quant-ph cs.LO}
} | sicard2005numerical |
arxiv-677318 | quant-ph/0504207 | Applications of quantum message sealing | <|reference_start|>Applications of quantum message sealing: In 2003, Bechmann-Pasquinucci introduced the concept of quantum seals, a quantum analogue to wax seals used to close letters and envelopes. Since then, some improvements on the method have been found. We first review the current quantum sealing techniques, then introduce and discuss potential applications of quantum message sealing, and conclude with some discussion of the limitations of quantum seals.<|reference_end|> | arxiv | @article{worley2005applications,
title={Applications of quantum message sealing},
author={G Gordon Worley III},
journal={arXiv preprint arXiv:quant-ph/0504207},
year={2005},
doi={10.1117/12.598260},
archivePrefix={arXiv},
eprint={quant-ph/0504207},
primaryClass={quant-ph cs.CR}
} | worley2005applications |
arxiv-677319 | quant-ph/0505088 | A Note on Shared Randomness and Shared Entanglement in Communication | <|reference_start|>A Note on Shared Randomness and Shared Entanglement in Communication: We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of simultaneous quantum message passing with shared randomness. We define a relation which can be efficiently exactly solved in the first model but cannot be solved efficiently, either exactly or in 0-error setup in the second model. In fact, our relation is exactly solvable even in a more restricted model of simultaneous classical message passing with shared entanglement. As our second contribution we strengthen a result by Yao that a "very short" protocol from the model of simultaneous classical message passing with shared randomness can be simulated in the model of simultaneous quantum message passing: for a boolean function f, QII(f) \in exp(O(RIIp(f))) log n. We show a similar result for protocols from a (stronger) model of 1-way classical message passing with shared randomness: QII(f) \in exp(O(RIp(f))) log n. We demonstrate a problem whose efficient solution in the model of simultaneous quantum message passing follows from our result but not from Yao's.<|reference_end|> | arxiv | @article{gavinsky2005a,
title={A Note on Shared Randomness and Shared Entanglement in Communication},
author={Dmytro Gavinsky (U Calgary)},
journal={arXiv preprint arXiv:quant-ph/0505088},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0505088},
primaryClass={quant-ph cs.CC}
} | gavinsky2005a |
arxiv-677320 | quant-ph/0505089 | Quantum key distribution with trusted quantum relay | <|reference_start|>Quantum key distribution with trusted quantum relay: A trusted quantum relay is introduced to enable quantum key distribution links to form the basic legs in a quantum key distribution network. The idea is based on the well-known intercept/resend eavesdropping. The same scheme can be used to make quantum key distribution between several parties. No entanglement is required.<|reference_end|> | arxiv | @article{bechmann-pasquinucci2005quantum,
title={Quantum key distribution with trusted quantum relay},
author={H. Bechmann-Pasquinucci and A. Pasquinucci},
journal={arXiv preprint arXiv:quant-ph/0505089},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0505089},
primaryClass={quant-ph cs.CR cs.NI}
} | bechmann-pasquinucci2005quantum |
arxiv-677321 | quant-ph/0505188 | Lower Bounds on Matrix Rigidity via a Quantum Argument | <|reference_start|>Lower Bounds on Matrix Rigidity via a Quantum Argument: The rigidity of a matrix measures how many of its entries need to be changed in order to reduce its rank to some value. Good lower bounds on the rigidity of an explicit matrix would imply good lower bounds for arithmetic circuits as well as for communication complexity. Here we reprove the best known bounds on the rigidity of Hadamard matrices, due to Kashin and Razborov, using tools from quantum computing. Our proofs are somewhat simpler than earlier ones (at least for those familiar with quantum) and give slightly better constants. More importantly, they give a new approach to attack this longstanding open problem.<|reference_end|> | arxiv | @article{de wolf2005lower,
title={Lower Bounds on Matrix Rigidity via a Quantum Argument},
author={Ronald de Wolf (CWI Amsterdam)},
journal={arXiv preprint arXiv:quant-ph/0505188},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0505188},
primaryClass={quant-ph cs.CC}
} | de wolf2005lower |
arxiv-677322 | quant-ph/0506080 | Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem | <|reference_start|>Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem: In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.<|reference_end|> | arxiv | @article{benatti2005entropy,
title={Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem},
author={Fabio Benatti, Tyll Krueger, Markus Mueller, Rainer Siegmund-Schultze,
Arleta Szkola},
journal={Communications in Mathematical Physics, Vol. 265, No.2 / July
2006, 437-461},
year={2005},
doi={10.1007/s00220-006-0027-z},
archivePrefix={arXiv},
eprint={quant-ph/0506080},
primaryClass={quant-ph cs.IT math-ph math.DS math.IT math.MP}
} | benatti2005entropy |
arxiv-677323 | quant-ph/0506200 | Solving Satisfiability Problems by the Ground-State Quantum Computer | <|reference_start|>Solving Satisfiability Problems by the Ground-State Quantum Computer: A quantum algorithm is proposed to solve the Satisfiability problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit Exact Cover problem. The time cost of this algorithm on the general SAT problems is discussed.<|reference_end|> | arxiv | @article{mao2005solving,
title={Solving Satisfiability Problems by the Ground-State Quantum Computer},
author={Wenjin Mao},
journal={Phys. Rev. A 72, 052316 (2005)},
year={2005},
doi={10.1103/PhysRevA.72.052316},
archivePrefix={arXiv},
eprint={quant-ph/0506200},
primaryClass={quant-ph cond-mat.mes-hall cs.CC}
} | mao2005solving |
arxiv-677324 | quant-ph/0506265 | Quantum Complexity of Testing Group Commutativity | <|reference_start|>Quantum Complexity of Testing Group Commutativity: We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in O (k^{2/3}). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Omega(k^{2/3}), we give a reduction from a special case of Element Distinctness to our problem. Along the way, we prove the optimality of the algorithm of Pak for the randomized model.<|reference_end|> | arxiv | @article{magniez2005quantum,
title={Quantum Complexity of Testing Group Commutativity},
author={Frederic Magniez (CNRS-LRI) and Ashwin Nayak (U. Waterloo and
Perimeter Inst.)},
journal={arXiv preprint arXiv:quant-ph/0506265},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0506265},
primaryClass={quant-ph cs.DS}
} | magniez2005quantum |
arxiv-677325 | quant-ph/0507155 | Theoretical Setting of Inner Reversible Quantum Measurements | <|reference_start|>Theoretical Setting of Inner Reversible Quantum Measurements: We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a unitary transformation on the state of the closed quantum system by means of a collection of generalized measurement operators. In particular, given a complete set of orthogonal projectors, it is possible to implement a reversible quantum measurement that preserves the probabilities. In this context, we introduce the concept of "Truth-Observable", which is the physical counterpart of an inner logical truth.<|reference_end|> | arxiv | @article{zizzi2005theoretical,
title={Theoretical Setting of Inner Reversible Quantum Measurements},
author={Paola Zizzi},
journal={Mod. Phys. Lett. A, Vol.21, No. 36 (2006) pp. 2717-2727},
year={2005},
doi={10.1142/S0217732306021827},
archivePrefix={arXiv},
eprint={quant-ph/0507155},
primaryClass={quant-ph cs.LO math-ph math.LO math.MP}
} | zizzi2005theoretical |
arxiv-677326 | quant-ph/0507231 | Algebras of Measurements: the logical structure of Quantum Mechanics | <|reference_start|>Algebras of Measurements: the logical structure of Quantum Mechanics: In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.<|reference_end|> | arxiv | @article{lehmann2005algebras,
title={Algebras of Measurements: the logical structure of Quantum Mechanics},
author={Daniel Lehmann, Kurt Engesser and Dov M. Gabbay},
journal={International Journal of Theoretical Physics, 45(4) April 2006,
pages 698-723},
year={2005},
doi={10.1007/s10773-006-9062-y},
number={TR 2005-91 Leibniz Center for Research in Computer Science, Hebrew
Un. Jerusalem},
archivePrefix={arXiv},
eprint={quant-ph/0507231},
primaryClass={quant-ph cs.AI}
} | lehmann2005algebras |
arxiv-677327 | quant-ph/0507234 | Grover's Quantum Search Algorithm and Diophantine Approximation | <|reference_start|>Grover's Quantum Search Algorithm and Diophantine Approximation: In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.<|reference_end|> | arxiv | @article{dolev2005grover's,
title={Grover's Quantum Search Algorithm and Diophantine Approximation},
author={Shahar Dolev, Itamar Pitowsky, and Boaz Tamir},
journal={Physical Review A 73 022308 (2006)},
year={2005},
doi={10.1103/PhysRevA.73.022308},
archivePrefix={arXiv},
eprint={quant-ph/0507234},
primaryClass={quant-ph cs.CC}
} | dolev2005grover's |
arxiv-677328 | quant-ph/0507270 | Quantum Minimal One Way Information: Relative Hardness and Quantum Advantage of Combinatorial Tasks | <|reference_start|>Quantum Minimal One Way Information: Relative Hardness and Quantum Advantage of Combinatorial Tasks: Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of instances, using one-way communication from another party. This type of complexity measure has been studied under various names: advice complexity, Kolmogorov complexity, distinguishing complexity, and instance complexity. We present a general framework focusing on underlying combinatorial takes to study these complexity measures using quantum information processing. We introduce the key notions of relative hardness and quantum advantage, which provide the foundations for task-based quantum minimal one-way information complexity theory.<|reference_end|> | arxiv | @article{nishimura2005quantum,
title={Quantum Minimal One Way Information: Relative Hardness and Quantum
Advantage of Combinatorial Tasks},
author={Harumichi Nishimura and Tomoyuki Yamakami},
journal={arXiv preprint arXiv:quant-ph/0507270},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0507270},
primaryClass={quant-ph cs.CC}
} | nishimura2005quantum |
arxiv-677329 | quant-ph/0508070 | Nonbinary stabilizer codes over finite fields | <|reference_start|>Nonbinary stabilizer codes over finite fields: One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been derived as binary stabilizer codes. Fault-tolerant quantum computation prompted the study of nonbinary quantum codes, but the theory of such codes is not as advanced as that of binary quantum codes. This paper describes the basic theory of stabilizer codes over finite fields. The relation between stabilizer codes and general quantum codes is clarified by introducing a Galois theory for these objects. A characterization of nonbinary stabilizer codes over GF(q) in terms of classical codes over GF(q^2) is provided that generalizes the well-known notion of additive codes over GF(4) of the binary case. This paper derives lower and upper bounds on the minimum distance of stabilizer codes, gives several code constructions, and derives numerous families of stabilizer codes, including quantum Hamming codes, quadratic residue codes, quantum Melas codes, quantum BCH codes, and quantum character codes. The puncturing theory by Rains is generalized to additive codes that are not necessarily pure. Bounds on the maximal length of maximum distance separable stabilizer codes are given. A discussion of open problems concludes this paper.<|reference_end|> | arxiv | @article{ketkar2005nonbinary,
title={Nonbinary stabilizer codes over finite fields},
author={Avanti Ketkar, Andreas Klappenecker, Santosh Kumar, Pradeep Kiran
Sarvepalli},
journal={arXiv preprint arXiv:quant-ph/0508070},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0508070},
primaryClass={quant-ph cs.IT math.IT}
} | ketkar2005nonbinary |
arxiv-677330 | quant-ph/0508072 | Generic Security Proof of Quantum Key Exchange using Squeezed States | <|reference_start|>Generic Security Proof of Quantum Key Exchange using Squeezed States: Recently, a Quantum Key Exchange protocol that uses squeezed states was presented by Gottesman and Preskill. In this paper we give a generic security proof for this protocol. The method used for this generic security proof is based on recent work by Christiandl, Renner and Ekert.<|reference_end|> | arxiv | @article{poels2005generic,
title={Generic Security Proof of Quantum Key Exchange using Squeezed States},
author={Karin Poels, Pim Tuyls, Berry Schoenmakers},
journal={arXiv preprint arXiv:quant-ph/0508072},
year={2005},
doi={10.1109/ISIT.2005.1523617},
archivePrefix={arXiv},
eprint={quant-ph/0508072},
primaryClass={quant-ph cs.CR}
} | poels2005generic |
arxiv-677331 | quant-ph/0508116 | A probabilistic branching bisimulation for quantum processes | <|reference_start|>A probabilistic branching bisimulation for quantum processes: Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts.Based upon an operational semantics which makes sure that quantum objects, operations and communications operate according to the postulates of quantum mechanics, a probabilistic branching bisimulation is defined among processes considered as having the same behavior.<|reference_end|> | arxiv | @article{lalire2005a,
title={A probabilistic branching bisimulation for quantum processes},
author={Marie Lalire},
journal={arXiv preprint arXiv:quant-ph/0508116},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0508116},
primaryClass={quant-ph cs.PL}
} | lalire2005a |
arxiv-677332 | quant-ph/0508149 | Variable Bias Coin Tossing | <|reference_start|>Variable Bias Coin Tossing: Alice is a charismatic quantum cryptographer who believes her parties are unmissable; Bob is a (relatively) glamorous string theorist who believes he is an indispensable guest. To prevent possibly traumatic collisions of self-perception and reality, their social code requires that decisions about invitation or acceptance be made via a cryptographically secure variable bias coin toss (VBCT). This generates a shared random bit by the toss of a coin whose bias is secretly chosen, within a stipulated range, by one of the parties; the other party learns only the random bit. Thus one party can secretly influence the outcome, while both can save face by blaming any negative decisions on bad luck. We describe here some cryptographic VBCT protocols whose security is guaranteed by quantum theory and the impossibility of superluminal signalling, setting our results in the context of a general discussion of secure two-party computation. We also briefly discuss other cryptographic applications of VBCT.<|reference_end|> | arxiv | @article{colbeck2005variable,
title={Variable Bias Coin Tossing},
author={Roger Colbeck and Adrian Kent (Centre for Quantum Computation, DAMTP,
University of Cambridge)},
journal={Phys. Rev. A 73, 032320 (2006)},
year={2005},
doi={10.1103/PhysRevA.73.032320},
archivePrefix={arXiv},
eprint={quant-ph/0508149},
primaryClass={quant-ph cs.CR}
} | colbeck2005variable |
arxiv-677333 | quant-ph/0508200 | A new quantum lower bound method, with an application to strong direct product theorem for quantum search | <|reference_start|>A new quantum lower bound method, with an application to strong direct product theorem for quantum search: We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product theorem for quantum search. This result was previously proven by Klauck, Spalek and de Wolf (quant-ph/0402123) using polynomials method. No proof using adversary method was known before.<|reference_end|> | arxiv | @article{ambainis2005a,
title={A new quantum lower bound method, with an application to strong direct
product theorem for quantum search},
author={Andris Ambainis},
journal={arXiv preprint arXiv:quant-ph/0508200},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0508200},
primaryClass={quant-ph cs.CC}
} | ambainis2005a |
arxiv-677334 | quant-ph/0508201 | Entanglement in Interactive Proof Systems with Binary Answers | <|reference_start|>Entanglement in Interactive Proof Systems with Binary Answers: If two classical provers share an entangled state, the resulting interactive proof system is significantly weakened [quant-ph/0404076]. We show that for the case where the verifier computes the XOR of two binary answers, the resulting proof system is in fact no more powerful than a system based on a single quantum prover: +MIP*[2] is contained in QIP(2). This also implies that +MIP*[2] is contained in EXP which was previously shown using a different method [Presentation of Cleve et al. at CCC'04]. This contrasts with an interactive proof system where the two provers do not share entanglement. In that case, +MIP[2] = NEXP for certain soundness and completeness parameters [quant-ph/0404076].<|reference_end|> | arxiv | @article{wehner2005entanglement,
title={Entanglement in Interactive Proof Systems with Binary Answers},
author={Stephanie Wehner (CWI, Amsterdam)},
journal={Proc. of 23rd STACS, 2006, LNCS 3884, pages 162-171.},
year={2005},
doi={10.1007/11672142_12},
archivePrefix={arXiv},
eprint={quant-ph/0508201},
primaryClass={quant-ph cs.CC}
} | wehner2005entanglement |
arxiv-677335 | quant-ph/0508222 | Cryptography In the Bounded Quantum-Storage Model | <|reference_start|>Cryptography In the Bounded Quantum-Storage Model: We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory, whereas an adversarial player needs quantum memory of size at least n/2 in order to break the protocol, where n is the number of qubits transmitted. This is in sharp contrast to the classical bounded-memory model, where we can only tolerate adversaries with memory of size quadratic in honest players' memory size. Our protocols are efficient, non-interactive and can be implemented using today's technology. On the technical side, a new entropic uncertainty relation involving min-entropy is established.<|reference_end|> | arxiv | @article{damgaard2005cryptography,
title={Cryptography In the Bounded Quantum-Storage Model},
author={Ivan Damgaard, Serge Fehr, Louis Salvail, Christian Schaffner},
journal={Proceedings of the 46th IEEE Symposium on Foundations of Computer
Science - FOCS 2005, pages 449-458},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0508222},
primaryClass={quant-ph cs.CR}
} | damgaard2005cryptography |
arxiv-677336 | quant-ph/0510031 | Image compression and entanglement | <|reference_start|>Image compression and entanglement: The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that quantum entanglement corresponds to classical correlations between different coarse-grained textures. A truncation of the MPS representation is tantamount to a compression of the original image. The resulting algorithm can be improved adding a discrete Fourier transform preprocessing and a further entropic lossless compression.<|reference_end|> | arxiv | @article{latorre2005image,
title={Image compression and entanglement},
author={Jose I. Latorre},
journal={arXiv preprint arXiv:quant-ph/0510031},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0510031},
primaryClass={quant-ph cs.MM}
} | latorre2005image |
arxiv-677337 | quant-ph/0510230 | QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols | <|reference_start|>QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols: This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomial-size quantum state, in such a way that the value of any one of those bits can later be proven with the help of a polynomial-size quantum witness. We also show that any problem in QMA with polynomial-size quantum advice, is also in PSPACE with polynomial-size classical advice. This builds on our earlier result that BQP/qpoly is contained in PP/poly, and offers an intriguing counterpoint to the recent discovery of Raz that QIP/qpoly = ALL. Finally, we show that QCMA/qpoly is contained in PP/poly and that QMA/rpoly = QMA/poly.<|reference_end|> | arxiv | @article{aaronson2005qma/qpoly,
title={QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols},
author={Scott Aaronson},
journal={arXiv preprint arXiv:quant-ph/0510230},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0510230},
primaryClass={quant-ph cs.CC}
} | aaronson2005qma/qpoly |
arxiv-677338 | quant-ph/0511013 | Bounded-Error Quantum State Identification and Exponential Separations in Communication Complexity | <|reference_start|>Bounded-Error Quantum State Identification and Exponential Separations in Communication Complexity: We consider the problem of bounded-error quantum state identification: given either state \alpha_0 or state \alpha_1, we are required to output `0', `1' or `?' ("don't know"), such that conditioned on outputting `0' or `1', our guess is correct with high probability. The goal is to maximize the probability of not outputting `?'. We prove a direct product theorem: if we're given two such problems, with optimal probabilities a and b, respectively, and the states in the first problem are pure, then the optimal probability for the joint bounded-error state identification problem is O(ab). Our proof is based on semidefinite programming duality and may be of wider interest. Using this result, we present two exponential separations in the simultaneous message passing model of communication complexity. Both are shown in the strongest possible sense. First, we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared randomness, but needs Omega(n^{1/3}) communication if the parties don't share randomness, even if communication is quantum. This shows the optimality of Yao's recent exponential simulation of shared-randomness protocols by quantum protocols without shared randomness. Second, we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared entanglement, but needs Omega((n/log n)^{1/3}) communication if the parties share randomness but no entanglement, even if communication is quantum. This is the first example in communication complexity of a situation where entanglement buys you much more than quantum communication does.<|reference_end|> | arxiv | @article{gavinsky2005bounded-error,
title={Bounded-Error Quantum State Identification and Exponential Separations
in Communication Complexity},
author={Dmytro Gavinsky, Julia Kempe, Oded Regev and Ronald de Wolf},
journal={arXiv preprint arXiv:quant-ph/0511013},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0511013},
primaryClass={quant-ph cs.CC}
} | gavinsky2005bounded-error |
arxiv-677339 | quant-ph/0511016 | Convolutional and tail-biting quantum error-correcting codes | <|reference_start|>Convolutional and tail-biting quantum error-correcting codes: Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding algorithms are derived from these convolutional codes via tail-biting.<|reference_end|> | arxiv | @article{forney,2005convolutional,
title={Convolutional and tail-biting quantum error-correcting codes},
author={G. David Forney, Jr., Markus Grassl, and Saikat Guha},
journal={IEEE Transactions on Information Theory, vol. 53, no. 3, March
2007, pp. 865-880},
year={2005},
doi={10.1109/TIT.2006.890698},
archivePrefix={arXiv},
eprint={quant-ph/0511016},
primaryClass={quant-ph cs.IT math.IT}
} | forney,2005convolutional |
arxiv-677340 | quant-ph/0511025 | Quantum Weakly Nondeterministic Communication Complexity | <|reference_start|>Quantum Weakly Nondeterministic Communication Complexity: We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function. This separation is quadratic.<|reference_end|> | arxiv | @article{gall2005quantum,
title={Quantum Weakly Nondeterministic Communication Complexity},
author={Francois Le Gall},
journal={Theoretical Computer Science, Vol. 486, pp. 43-49, 2013},
year={2005},
doi={10.1016/j.tcs.2012.12.015},
archivePrefix={arXiv},
eprint={quant-ph/0511025},
primaryClass={quant-ph cs.CC}
} | gall2005quantum |
arxiv-677341 | quant-ph/0511145 | Semantics and simulation of communication in quantum programming | <|reference_start|>Semantics and simulation of communication in quantum programming: We present the quantum programming language cQPL which is an extended version of QPL [P. Selinger, Math. Struct. in Comp. Sci. 14(4):527-586, 2004]. It is capable of quantum communication and it can be used to formulate all possible quantum algorithms. Additionally, it possesses a denotational semantics based on a partial order of superoperators and uses fixed points on a generalised Hilbert space to formalise (in addition to all standard features expected from a quantum programming language) the exchange of classical and quantum data between an arbitrary number of participants. Additionally, we present the implementation of a cQPL compiler which generates code for a quantum simulator.<|reference_end|> | arxiv | @article{mauerer2005semantics,
title={Semantics and simulation of communication in quantum programming},
author={Wolfgang Mauerer},
journal={arXiv preprint arXiv:quant-ph/0511145},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0511145},
primaryClass={quant-ph cs.PL}
} | mauerer2005semantics |
arxiv-677342 | quant-ph/0511148 | Limitations of Quantum Coset States for Graph Isomorphism | <|reference_start|>Limitations of Quantum Coset States for Graph Isomorphism: It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard it is to use these states to solve graph isomorphism. It was recently shown by Moore, Russell, and Schulman that only an exponentially small amount of information is available from one, or a pair of coset states. A potential source of power to exploit are entangled quantum measurements that act jointly on many states at once. We show that entangled quantum measurements on at least \Omega(n log n) coset states are necessary to get useful information for the case of graph isomorphism, matching an information theoretic upper bound. This may be viewed as a negative result because highly entangled measurements seem hard to implement in general. Our main theorem is very general and also rules out using joint measurements on few coset states for some other groups, such as GL(n, F_{p^m}) and G^n where G is finite and satisfies a suitable property.<|reference_end|> | arxiv | @article{hallgren2005limitations,
title={Limitations of Quantum Coset States for Graph Isomorphism},
author={Sean Hallgren, Martin Roetteler, and Pranab Sen},
journal={J. ACM 57(6): 34 (2010)},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0511148},
primaryClass={quant-ph cs.ET}
} | hallgren2005limitations |
arxiv-677343 | quant-ph/0511172 | On Classical Teleportation and Classical Nonlocality | <|reference_start|>On Classical Teleportation and Classical Nonlocality: An interesting protocol for classical teleportation of an unknown classical state was recently suggested by Cohen, and by Gour and Meyer. In that protocol, Bob can sample from a probability distribution P that is given to Alice, even if Alice has absolutely no knowledge about P. Pursuing a similar line of thought, we suggest here a limited form of nonlocality - "classical nonlocality". Our nonlocality is the (somewhat limited) classical analogue of the Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocality tells us how, for a given density matrix rho, Alice can generate any rho-ensemble on the North Star. This is done using surprisingly few resources - one shared entangled state (prepared in advance), one generalized quantum measurement, and no communication. Similarly, our classical nonlocality presents how, for a given probability distribution P, Alice can generate any P-ensemble on the North Star, using only one correlated state (prepared in advance), one (generalized) classical measurement, and no communication. It is important to clarify that while the classical teleportation and the classical non-locality protocols are probably rather insignificant from a classical information processing point of view, they significantly contribute to our understanding of what exactly is quantum in their well established and highly famous quantum analogues.<|reference_end|> | arxiv | @article{mor2005on,
title={On Classical Teleportation and Classical Nonlocality},
author={Tal Mor},
journal={Int. J. of Quantum Information 4, 161-172 (2006)},
year={2005},
doi={10.1063/1.2165638},
archivePrefix={arXiv},
eprint={quant-ph/0511172},
primaryClass={quant-ph cs.IT math.IT}
} | mor2005on |
arxiv-677344 | quant-ph/0511175 | A Proof of the Security of Quantum Key Distribution | <|reference_start|>A Proof of the Security of Quantum Key Distribution: We prove the security of theoretical quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages such that their security is also unaffected in the future.<|reference_end|> | arxiv | @article{biham2005a,
title={A Proof of the Security of Quantum Key Distribution},
author={Eli Biham, Michel Boyer, P. Oscar Boykin, Tal Mor and Vwani
Roychowdhury},
journal={Journal of cryptology 19, 381-439 (2006)},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0511175},
primaryClass={quant-ph cs.CR cs.IT math.IT}
} | biham2005a |
arxiv-677345 | quant-ph/0511200 | A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs | <|reference_start|>A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs: We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct product theorem for 2-sided error quantum algorithms computing k independent instances of a symmetric Boolean function: if the algorithm uses significantly less than k times the number of queries needed for one instance of the function, then its success probability is exponentially small in k. We also use the polynomial method to prove a direct product theorem for 1-sided error algorithms for k threshold functions with a stronger bound on the success probability. Finally, we present a quantum algorithm for evaluating solutions to systems of linear inequalities, and use our direct product theorems to show that the time-space tradeoff of this algorithm is close to optimal.<|reference_end|> | arxiv | @article{ambainis2005a,
title={A New Quantum Lower Bound Method, with Applications to Direct Product
Theorems and Time-Space Tradeoffs},
author={Andris Ambainis (U Waterloo), Robert Spalek (CWI), Ronald de Wolf
(CWI)},
journal={arXiv preprint arXiv:quant-ph/0511200},
year={2005},
archivePrefix={arXiv},
eprint={quant-ph/0511200},
primaryClass={quant-ph cs.CC}
} | ambainis2005a |
arxiv-677346 | quant-ph/0511272 | Quantum Advantage without Entanglement | <|reference_start|>Quantum Advantage without Entanglement: We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm still has an advantage over the classical ones. We further show that this subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and Grover's algorithms we provide simple proofs that no non-trivial subproblems can be solved by these algorithms without entanglement.<|reference_end|> | arxiv | @article{kenigsberg2005quantum,
title={Quantum Advantage without Entanglement},
author={Dan Kenigsberg, Tal Mor and Gil Ratsaby},
journal={Quantum Information and Computation 6(7), 606--615 (2006)},
year={2005},
doi={10.1117/12.617175},
archivePrefix={arXiv},
eprint={quant-ph/0511272},
primaryClass={quant-ph cs.CC}
} | kenigsberg2005quantum |
arxiv-677347 | quant-ph/0512114 | A Categorical Quantum Logic | <|reference_start|>A Categorical Quantum Logic: We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a given category with an involution. This syntax can be used to represent and reason about quantum processes.<|reference_end|> | arxiv | @article{abramsky2005a,
title={A Categorical Quantum Logic},
author={Samson Abramsky, Ross Duncan},
journal={arXiv preprint arXiv:quant-ph/0512114},
year={2005},
doi={10.1017/S0960129506005275},
archivePrefix={arXiv},
eprint={quant-ph/0512114},
primaryClass={quant-ph cs.LO}
} | abramsky2005a |
arxiv-677348 | quant-ph/0601115 | Phase-Remapping Attack in Practical Quantum Key Distribution Systems | <|reference_start|>Phase-Remapping Attack in Practical Quantum Key Distribution Systems: Quantum key distribution (QKD) can be used to generate secret keys between two distant parties. Even though QKD has been proven unconditionally secure against eavesdroppers with unlimited computation power, practical implementations of QKD may contain loopholes that may lead to the generated secret keys being compromised. In this paper, we propose a phase-remapping attack targeting two practical bidirectional QKD systems (the "plug & play" system and the Sagnac system). We showed that if the users of the systems are unaware of our attack, the final key shared between them can be compromised in some situations. Specifically, we showed that, in the case of the Bennett-Brassard 1984 (BB84) protocol with ideal single-photon sources, when the quantum bit error rate (QBER) is between 14.6% and 20%, our attack renders the final key insecure, whereas the same range of QBER values has been proved secure if the two users are unaware of our attack; also, we demonstrated three situations with realistic devices where positive key rates are obtained without the consideration of Trojan horse attacks but in fact no key can be distilled. We remark that our attack is feasible with only current technology. Therefore, it is very important to be aware of our attack in order to ensure absolute security. In finding our attack, we minimize the QBER over individual measurements described by a general POVM, which has some similarity with the standard quantum state discrimination problem.<|reference_end|> | arxiv | @article{fung2006phase-remapping,
title={Phase-Remapping Attack in Practical Quantum Key Distribution Systems},
author={Chi-Hang Fred Fung, Bing Qi, Kiyoshi Tamaki, and Hoi-Kwong Lo (Center
for Quantum Information and Quantum Control, University of Toronto, and NTT
Basic Research Laboratories, NTT Corporation)},
journal={Phys. Rev. A 75, 032314 (2007)},
year={2006},
doi={10.1103/PhysRevA.75.032314},
archivePrefix={arXiv},
eprint={quant-ph/0601115},
primaryClass={quant-ph cs.IT math.IT}
} | fung2006phase-remapping |
arxiv-677349 | quant-ph/0602063 | Topological Quantum Error Correction with Optimal Encoding Rate | <|reference_start|>Topological Quantum Error Correction with Optimal Encoding Rate: We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.<|reference_end|> | arxiv | @article{bombin2006topological,
title={Topological Quantum Error Correction with Optimal Encoding Rate},
author={H. Bombin, M.A. Martin-Delgado},
journal={Phys.Rev.A73:062303,2006},
year={2006},
doi={10.1103/PhysRevA.73.062303},
archivePrefix={arXiv},
eprint={quant-ph/0602063},
primaryClass={quant-ph cond-mat.str-el cs.GR hep-th math-ph math.AT math.CO math.MP}
} | bombin2006topological |
arxiv-677350 | quant-ph/0602087 | A quantum secret ballot | <|reference_start|>A quantum secret ballot: The paper concerns the protection of the secrecy of ballots, so that the identity of the voters cannot be matched with their vote. To achieve this we use an entangled quantum state to represent the ballots. Each ballot includes the identity of the voter, explicitly marked on the "envelope" containing it. Measuring the content of the envelope yields a random number which reveals no information about the vote. However, the outcome of the elections can be unambiguously decided after adding the random numbers from all envelopes. We consider a few versions of the protocol and their complexity of implementation.<|reference_end|> | arxiv | @article{dolev2006a,
title={A quantum secret ballot},
author={Shahar Dolev, Itamar Pitowsky, Boaz Tamir},
journal={arXiv preprint arXiv:quant-ph/0602087},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0602087},
primaryClass={quant-ph cs.CC}
} | dolev2006a |
arxiv-677351 | quant-ph/0602088 | Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding | <|reference_start|>Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding: Hardcore functions have been used as a technical tool to construct secure cryptographic systems; however, little is known on their quantum counterpart, called quantum hardcore functions. With a new insight into fundamental properties of quantum hardcores, we present three new quantum hardcore functions for any (strong) quantum one-way function. We also give a "quantum" solution to Damgard's question (CRYPTO'88) on a classical hardcore property of his pseudorandom generator, by proving its quantum hardcore property. Our major technical tool is the new notion of quantum list-decoding of "classical" error-correcting codes (rather than "quantum" error-correcting codes), which is defined on the platform of computational complexity theory and computational cryptography (rather than information theory). In particular, we give a simple but powerful criterion that makes a polynomial-time computable classical block code (seen as a function) a quantum hardcore for all quantum one-way functions. On their own interest, we construct efficient quantum list-decoding algorithms for classical block codes whose associated quantum states (called codeword states) form a nearly phase-orthogonal basis.<|reference_end|> | arxiv | @article{kawachi2006quantum,
title={Quantum Hardcore Functions by Complexity-Theoretical Quantum List
Decoding},
author={Akinori Kawachi and Tomoyuki Yamakami},
journal={(journal version) SIAM Journal on Computing, Vol.39, pp.2941-2969,
2010},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0602088},
primaryClass={quant-ph cs.CC}
} | kawachi2006quantum |
arxiv-677352 | quant-ph/0602114 | The quantum measurement problem and physical reality: a computation theoretic perspective | <|reference_start|>The quantum measurement problem and physical reality: a computation theoretic perspective: Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.<|reference_end|> | arxiv | @article{srikanth2006the,
title={The quantum measurement problem and physical reality: a computation
theoretic perspective},
author={R. Srikanth},
journal={AIP Conference Proceedings 864, pp. 178-193 (2006)},
year={2006},
doi={10.1063/1.2400889},
archivePrefix={arXiv},
eprint={quant-ph/0602114},
primaryClass={quant-ph cs.CC}
} | srikanth2006the |
arxiv-677353 | quant-ph/0602129 | Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes | <|reference_start|>Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes: We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic encoders derived in a paper by Ollivier and Tillich (quant-ph/0401134) which are applicable only for a restricted class of quantum convolutional codes. We also show that the encoders and their inverses constructed by our method naturally can be applied online, i.e., qubits can be sent and received with constant delay.<|reference_end|> | arxiv | @article{grassl2006non-catastrophic,
title={Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional
Codes},
author={Markus Grassl and Martin Roetteler},
journal={Proceedings 2006 IEEE International Symposium on Information
Theory, pp. 1109-1113},
year={2006},
doi={10.1109/ISIT.2006.261956},
archivePrefix={arXiv},
eprint={quant-ph/0602129},
primaryClass={quant-ph cs.IT math.IT}
} | grassl2006non-catastrophic |
arxiv-677354 | quant-ph/0602156 | Quantum Predicative Programming | <|reference_start|>Quantum Predicative Programming: The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the well-established predicative programming. It supports the style of program development in which each programming step is proven correct as it is made. We inherit the advantages of the theory, such as its generality, simple treatment of recursive programs, time and space complexity, and communication. Our theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.<|reference_end|> | arxiv | @article{tafliovich2006quantum,
title={Quantum Predicative Programming},
author={Anya Tafliovich, E.C.R. Hehner},
journal={arXiv preprint arXiv:quant-ph/0602156},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0602156},
primaryClass={quant-ph cs.PL}
} | tafliovich2006quantum |
arxiv-677355 | quant-ph/0603031 | Channel capacities of classical and quantum list decoding | <|reference_start|>Channel capacities of classical and quantum list decoding: We focus on classical and quantum list decoding. The capacity of list decoding was obtained by Nishimura in the case when the number of list does not increase exponentially. However, the capacity of the exponential-list case is open even in the classical case while its converse part was obtained by Nishimura. We derive the channel capacities in the classical and quantum case with an exponentially increasing list. The converse part of the quantum case is obtained by modifying Nagaoka's simple proof for strong converse theorem for channel capacity. The direct part is derived by a quite simple argument.<|reference_end|> | arxiv | @article{hayashi2006channel,
title={Channel capacities of classical and quantum list decoding},
author={Masahito Hayashi},
journal={arXiv preprint arXiv:quant-ph/0603031},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0603031},
primaryClass={quant-ph cs.IT math.IT}
} | hayashi2006channel |
arxiv-677356 | quant-ph/0603034 | New upper and lower bounds for randomized and quantum Local Search | <|reference_start|>New upper and lower bounds for randomized and quantum Local Search: Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer science. In this paper, we study the problem in the randomized and quantum query models and give new lower and upper bound techniques in both models. The lower bound technique works for any graph that contains a product graph as a subgraph. Applying it to the Boolean hypercube {0,1}^n and the constant dimensional grids [n]^d, two particular product graphs that recently drew much attention, we get the following tight results: RLS({0,1}^n) = \Theta(2^{n/2}n^{1/2}), QLS({0,1}^n) = \Theta(2^{n/3}n^{1/6}), RLS([n]^d) = \Theta(n^{d/2}) for d \geq 4, QLS([n]^d) = \Theta(n^{d/3}) for d \geq 6. Here RLS(G) and QLS(G) are the randomized and quantum query complexities of Local Search on G, respectively. These improve the previous results by Aaronson [STOC'04], Ambainis (unpublished) and Santha and Szegedy [STOC'04]. Our new algorithms work well when the underlying graph expands slowly. As an application to [n]^2, a new quantum algorithm using O(\sqrt{n}(\log\log n)^{1.5}) queries is given. This improves the previous best known upper bound of O(n^{2/3}) (Aaronson, [STOC'04]), and implies that Local Search on grids exhibits different properties in low dimensions.<|reference_end|> | arxiv | @article{zhang2006new,
title={New upper and lower bounds for randomized and quantum Local Search},
author={Shengyu Zhang},
journal={arXiv preprint arXiv:quant-ph/0603034},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0603034},
primaryClass={quant-ph cs.CC}
} | zhang2006new |
arxiv-677357 | quant-ph/0603098 | Quantum broadcast channels | <|reference_start|>Quantum broadcast channels: We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pairs of parties with the assistance of free classical communication.<|reference_end|> | arxiv | @article{yard2006quantum,
title={Quantum broadcast channels},
author={Jon Yard, Patrick Hayden, Igor Devetak},
journal={arXiv preprint arXiv:quant-ph/0603098},
year={2006},
doi={10.1109/TIT.2011.2165811},
archivePrefix={arXiv},
eprint={quant-ph/0603098},
primaryClass={quant-ph cs.IT math.IT}
} | yard2006quantum |
arxiv-677358 | quant-ph/0603135 | Interaction in Quantum Communication | <|reference_start|>Interaction in Quantum Communication: In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges between the communicating parties. It is therefore natural to ask whether every classical protocol may be transformed to a ``simpler'' quantum protocol--one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity. This, in particular, proves a round hierarchy theorem for quantum communication complexity, and implies, via a simple reduction, an Omega(N^{1/k}) lower bound for k message quantum protocols for Set Disjointness for constant k. Enroute, we prove information-theoretic lemmas, and define a related measure of correlation, the informational distance, that we believe may be of significance in other contexts as well.<|reference_end|> | arxiv | @article{klauck2006interaction,
title={Interaction in Quantum Communication},
author={Hartmut Klauck, Ashwin Nayak, Amnon Ta-Shma and David Zuckerman},
journal={arXiv preprint arXiv:quant-ph/0603135},
year={2006},
doi={10.1109/TIT.2007.896888},
archivePrefix={arXiv},
eprint={quant-ph/0603135},
primaryClass={quant-ph cs.CC cs.IT math.IT}
} | klauck2006interaction |
arxiv-677359 | quant-ph/0603173 | Strengths and Weaknesses of Quantum Fingerprinting | <|reference_start|>Strengths and Weaknesses of Quantum Fingerprinting: We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness ($Q^\parallel$-protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by $Q^\parallel$-protocols. We apply our technique to obtain an efficient $Q^\parallel$-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.<|reference_end|> | arxiv | @article{gavinsky2006strengths,
title={Strengths and Weaknesses of Quantum Fingerprinting},
author={Dmytro Gavinsky, Julia Kempe, Ronald de Wolf},
journal={Proc. 21st CCC (Complexity), p. 288-295 (2006)},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0603173},
primaryClass={quant-ph cs.CC}
} | gavinsky2006strengths |
arxiv-677360 | quant-ph/0603199 | Computational complexity of the quantum separability problem | <|reference_start|>Computational complexity of the quantum separability problem: Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic (as opposed to randomized) computational complexity. First, I review the one-sided tests for separability, paying particular attention to the semidefinite programming methods. Then, I discuss various ways of formulating the quantum separability problem, from exact to approximate formulations, the latter of which are the paper's main focus. I then give a thorough treatment of the problem's relationship with the complexity classes NP, NP-complete, and co-NP. I also discuss extensions of Gurvits' NP-hardness result to strong NP-hardness of certain related problems. A major open question is whether the NP-contained formulation (QSEP) of the quantum separability problem is Karp-NP-complete; QSEP may be the first natural example of a problem that is Turing-NP-complete but not Karp-NP-complete. Finally, I survey all the proposed (deterministic) algorithms for the quantum separability problem, including the bounded search for symmetric extensions (via semidefinite programming), based on the recent quantum de Finetti theorem; and the entanglement-witness search (via interior-point algorithms and global optimization). These two algorithms have the lowest complexity, with the latter being the best under advice of asymptotically optimal point-coverings of the sphere.<|reference_end|> | arxiv | @article{ioannou2006computational,
title={Computational complexity of the quantum separability problem},
author={Lawrence M. Ioannou},
journal={Quantum Information and Computation, Vol. 7, No. 4 (2007) 335-370},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0603199},
primaryClass={quant-ph cs.CC}
} | ioannou2006computational |
arxiv-677361 | quant-ph/0604013 | Beyond iid in Quantum Information Theory | <|reference_start|>Beyond iid in Quantum Information Theory: The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this paper the quantum spectral divergence rates are defined and properties of the rates are derived. The entropic rates, conditional entropic rates, and spectral mutual information rates are then defined in terms of the spectral divergence rates. Properties including subadditivity, chain rules, Araki-Lieb inequalities, and monotonicity are then explored.<|reference_end|> | arxiv | @article{bowen2006beyond,
title={Beyond i.i.d. in Quantum Information Theory},
author={Garry Bowen and Nilanjana Datta},
journal={arXiv preprint arXiv:quant-ph/0604013},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0604013},
primaryClass={quant-ph cs.IT math.IT}
} | bowen2006beyond |
arxiv-677362 | quant-ph/0604052 | On the Role of Shared Entanglement | <|reference_start|>On the Role of Shared Entanglement: Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for the famous theorem by Newman, saying that the number of shared random bits required for solving any communication problem can be at most logarithmic in the input length (i.e., using more than O(log n) shared random bits would not reduce the complexity of an optimal solution). In this paper we prove that the same is not true for entanglement. We establish a wide range of tight (up to a polylogarithmic factor) entanglement vs. communication tradeoffs for relational problems. The low end is: for any t>2, reducing shared entanglement from log^t(n) to o(log^{t-2}(n)) qubits can increase the communication required for solving a problem almost exponentially, from O(log^t(n)) to \Omega(\sqrt n). The high end is: for any \eps>0, reducing shared entanglement from n^{1-\eps}log(n) to o(n^{1-\eps}/log(n)) can increase the required communication from O(n^{1-\eps}log(n)) to \Omega(n^{1-\eps/2}/log(n)). The upper bounds are demonstrated via protocols which are exact and work in the \e{simultaneous message passing model}, while the lower bounds hold for \e{bounded-error protocols}, even in the more powerful \e{model of 1-way communication}. Our protocols use shared EPR pairs while the lower bounds apply to any sort of prior entanglement. We base the lower bounds on a strong direct product theorem for communication complexity of a certain class of relational problems. We believe that the theorem might have applications outside the scope of this work.<|reference_end|> | arxiv | @article{gavinsky2006on,
title={On the Role of Shared Entanglement},
author={Dmytro Gavinsky},
journal={arXiv preprint arXiv:quant-ph/0604052},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0604052},
primaryClass={quant-ph cs.CC}
} | gavinsky2006on |
arxiv-677363 | quant-ph/0604056 | Quantum Versus Classical Proofs and Advice | <|reference_start|>Quantum Versus Classical Proofs and Advice: This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More concretely, we show that any quantum algorithm needs $\Omega(\sqrt{2^n/(m+1)})$ queries to find an $n$-qubit "marked state" $\lvert\psi\rangle$, even if given an $m$-bit classical description of $\lvert\psi\rangle$ together with a quantum black box that recognizes $\lvert\psi\rangle$. Second, we give an explicit QCMA protocol that nearly achieves this lower bound. Third, we show that, in the one previously-known case where quantum proofs seemed to provide an exponential advantage, classical proofs are basically just as powerful. In particular, Watrous gave a QMA protocol for verifying non-membership in finite groups. Under plausible group-theoretic assumptions, we give a QCMA protocol for the same problem. Even with no assumptions, our protocol makes only polynomially many queries to the group oracle. We end with some conjectures about quantum versus classical oracles, and about the possibility of a classical oracle separation between QMA and QCMA.<|reference_end|> | arxiv | @article{aaronson2006quantum,
title={Quantum Versus Classical Proofs and Advice},
author={Scott Aaronson and Greg Kuperberg},
journal={Theory Comput. 3 (2007), 129-157},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0604056},
primaryClass={quant-ph cs.CC}
} | aaronson2006quantum |
arxiv-677364 | quant-ph/0604161 | Clifford Code Constructions of Operator Quantum Error Correcting Codes | <|reference_start|>Clifford Code Constructions of Operator Quantum Error Correcting Codes: Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabilizer codes due to Knill. Character-theoretic methods are used to derive a simple method to construct operator quantum error-correcting codes from any classical additive code over a finite field.<|reference_end|> | arxiv | @article{klappenecker2006clifford,
title={Clifford Code Constructions of Operator Quantum Error Correcting Codes},
author={Andreas Klappenecker and Pradeep Kiran Sarvepalli},
journal={arXiv preprint arXiv:quant-ph/0604161},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0604161},
primaryClass={quant-ph cs.IT math.IT}
} | klappenecker2006clifford |
arxiv-677365 | quant-ph/0605030 | Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity | <|reference_start|>Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity: We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that there is a UQTM that can simulate every other QTM for an arbitrary, but preassigned number of time steps. As a corollary to this result, we give a rigorous proof that quantum Kolmogorov complexity as defined by Berthiaume et al. is invariant, i.e. depends on the choice of the UQTM only up to an additive constant. Our proof is based on a new mathematical framework for QTMs, including a thorough analysis of their halting behaviour. We introduce the notion of mutually orthogonal halting spaces and show that the information encoded in an input qubit string can always be effectively decomposed into a classical and a quantum part.<|reference_end|> | arxiv | @article{mueller2006strongly,
title={Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov
Complexity},
author={Markus Mueller},
journal={IEEE Trans. Inf. Th., Vol. 54/2 pp. 763-780 (2008)},
year={2006},
doi={10.1109/TIT.2007.913263},
archivePrefix={arXiv},
eprint={quant-ph/0605030},
primaryClass={quant-ph cs.IT math-ph math.IT math.MP}
} | mueller2006strongly |
arxiv-677366 | quant-ph/0605041 | Invertible Quantum Operations and Perfect Encryption of Quantum States | <|reference_start|>Invertible Quantum Operations and Perfect Encryption of Quantum States: In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the ``private quantum channels'' studied by Ambainis, Mosca, Tapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.<|reference_end|> | arxiv | @article{nayak2006invertible,
title={Invertible Quantum Operations and Perfect Encryption of Quantum States},
author={Ashwin Nayak (1), Pranab Sen (2) ((1) U. Waterloo & Perimeter, (2)
TIFR)},
journal={arXiv preprint arXiv:quant-ph/0605041},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0605041},
primaryClass={quant-ph cs.CR cs.IT math.IT}
} | nayak2006invertible |
arxiv-677367 | quant-ph/0605096 | Quantum Information and Entropy | <|reference_start|>Quantum Information and Entropy: Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.<|reference_end|> | arxiv | @article{kak2006quantum,
title={Quantum Information and Entropy},
author={Subhash Kak},
journal={International Journal of Theoretical Physics, vol. 46, pp.
860-876, 2007.},
year={2006},
doi={10.1007/s10773-006-9245-6},
archivePrefix={arXiv},
eprint={quant-ph/0605096},
primaryClass={quant-ph cs.IT math.IT}
} | kak2006quantum |
arxiv-677368 | quant-ph/0605150 | Using quantum oblivious transfer to cheat sensitive quantum bit commitment | <|reference_start|>Using quantum oblivious transfer to cheat sensitive quantum bit commitment: It is well known that unconditionally secure bit commitment is impossible even in the quantum world. In this paper a weak variant of quantum bit commitment, introduced independently by Aharonov et al. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] is investigated. In this variant, the parties require some nonzero probability of detecting a cheating, i.e. if Bob, who commits a bit b to Alice, changes his mind during the revealing phase then Alice detects the cheating with a positive probability (we call this property binding); and if Alice gains information about the committed bit before the revealing phase then Bob discovers this with positive probability (sealing). In our paper we give quantum bit commitment scheme that is simultaneously binding and sealing and we show that if a cheating gives epsilon advantage to a malicious Alice then Bob can detect the cheating with a probability Omega(epsilon^2). If Bob cheats then Alice's probability of detecting the cheating is greater than some fixed constant lambda>0. This improves the probabilities of cheating detections shown by Hardy and Kent and the scheme by Aharonov et al. who presented a protocol that is either binding or sealing, but not simultaneously both. To construct a cheat sensitive quantum bit commitment scheme we use a protocol for a weak quantum one-out-of-two oblivious transfer.<|reference_end|> | arxiv | @article{jakoby2006using,
title={Using quantum oblivious transfer to cheat sensitive quantum bit
commitment},
author={Andreas Jakoby, Maciej Liskiewicz, and Aleksander Madry},
journal={arXiv preprint arXiv:quant-ph/0605150},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0605150},
primaryClass={quant-ph cs.CR}
} | jakoby2006using |
arxiv-677369 | quant-ph/0605181 | The BQP-hardness of approximating the Jones Polynomial | <|reference_start|>The BQP-hardness of approximating the Jones Polynomial: A celebrated important result due to Freedman, Larsen and Wang states that providing additive approximations of the Jones polynomial at the k'th root of unity, for constant k=5 and k>6, is BQP-hard. Together with the algorithmic results of Freedman et al and Aharonov et al, this gives perhaps the most natural BQP-complete problem known today and motivates further study of the topic. In this paper we focus on the universality proof; we extend the universality result of Freedman et al to k's that grow polynomially with the number of strands and crossings in the link, thus extending the BQP-hardness of Jones polynomial approximations to all values for which the AJL algorithm applies, proving that for all those values, the problems are BQP-complete. As a side benefit, we derive a fairly elementary proof of the Freedman et al density result, without referring to advanced results from Lie algebra representation theory, making this important result accessible to computer science audience. We make use of two general lemmas we prove, the Bridge lemma and the Decoupling lemma, which provide tools for establishing density of subgroups in SU(n). Those tools seem to be of independent interest in more general contexts of proving quantum universality. Our result also implies a completely classical statement, that the_multiplicative_ approximations of the Jones polynomial, at exactly the same values, are #P-hard, via a recent result due to Kuperberg. Since the first publication of those results in their preliminary form (arXiv:quant-ph/0605181v2), the methods we present here were used in several other contexts. This paper is an improved and extended version of the original results, and also includes discussions of the developments since then.<|reference_end|> | arxiv | @article{aharonov2006the,
title={The BQP-hardness of approximating the Jones Polynomial},
author={Dorit Aharonov and Itai Arad},
journal={New J. Phys. 13 (2011) 035019},
year={2006},
doi={10.1088/1367-2630/13/3/035019},
archivePrefix={arXiv},
eprint={quant-ph/0605181},
primaryClass={quant-ph cs.CC}
} | aharonov2006the |
arxiv-677370 | quant-ph/0605182 | Maximally Non-Local and Monogamous Quantum Correlations | <|reference_start|>Maximally Non-Local and Monogamous Quantum Correlations: We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to give a simple proof that the maximally entangled state of two d dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental programme to obtain as good an upper bound as possible on the fraction of local states, and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among non-signalling correlations, and hence can be used for quantum key distribution secure against post-quantum (but non-signalling) eavesdroppers.<|reference_end|> | arxiv | @article{barrett2006maximally,
title={Maximally Non-Local and Monogamous Quantum Correlations},
author={Jonathan Barrett, Adrian Kent and Stefano Pironio},
journal={Phys. Rev. Lett. 97, 170409 (2006).},
year={2006},
doi={10.1103/PhysRevLett.97.170409},
archivePrefix={arXiv},
eprint={quant-ph/0605182},
primaryClass={quant-ph cs.CR}
} | barrett2006maximally |
arxiv-677371 | quant-ph/0605219 | Classical simulators of quantum computers and no-go theorems | <|reference_start|>Classical simulators of quantum computers and no-go theorems: It is discussed, why classical simulators of quantum computers escape from some no-go claims like Kochen-Specker, Bell, or recent Conway-Kochen "Free Will" theorems.<|reference_end|> | arxiv | @article{vlasov2006classical,
title={Classical simulators of quantum computers and no-go theorems},
author={Alexander Yu. Vlasov},
journal={arXiv preprint arXiv:quant-ph/0605219},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0605219},
primaryClass={quant-ph cs.OH}
} | vlasov2006classical |
arxiv-677372 | quant-ph/0606049 | Full security of quantum key distribution from no-signaling constraints | <|reference_start|>Full security of quantum key distribution from no-signaling constraints: We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any information accessible to them must be compatible with the non-signaling principle. The claim holds with respect to the state-of-the-art security definition used in cryptography, known as universally-composable security. The non-signaling assumption only refers to the statistics of measurement outcomes depending on the choices of measurements; hence security is independent of the internal workings of the devices --- they do not even need to follow the laws of quantum theory. This is relevant for practice as a correct and complete modeling of realistic devices is generally impossible. The techniques developed are general and can be applied to other Bell inequality-based protocols. In particular, we provide a scheme for estimating Bell-inequality violations when the samples are not independent and identically distributed.<|reference_end|> | arxiv | @article{masanes2006full,
title={Full security of quantum key distribution from no-signaling constraints},
author={Ll. Masanes, R. Renner, M. Christandl, A. Winter, J. Barrett},
journal={IEEE Transactions on Information Theory, Volume 60, Issue 8, pages
4973-4986, year 2014},
year={2006},
doi={10.1109/TIT.2014.2329417},
archivePrefix={arXiv},
eprint={quant-ph/0606049},
primaryClass={quant-ph cs.CR}
} | masanes2006full |
arxiv-677373 | quant-ph/0606066 | Exponential Separation of Quantum and Classical Online Space Complexity | <|reference_start|>Exponential Separation of Quantum and Classical Online Space Complexity: Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.<|reference_end|> | arxiv | @article{gall2006exponential,
title={Exponential Separation of Quantum and Classical Online Space Complexity},
author={Francois Le Gall},
journal={Theory of Computing Systems 45(2): 188-202 (2009)},
year={2006},
doi={10.1007/s00224-007-9097-3},
archivePrefix={arXiv},
eprint={quant-ph/0606066},
primaryClass={quant-ph cs.CC}
} | gall2006exponential |
arxiv-677374 | quant-ph/0607111 | `Plausibilities of plausibilities': an approach through circumstances | <|reference_start|>`Plausibilities of plausibilities': an approach through circumstances: Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a probability and that satisfies some additional logical properties. The idea, which can be traced to Laplace and Jaynes, is that the usual inferential reasonings about the probability-like parameters of a statistical model can be conceived as reasonings about equivalence classes of `circumstances' - viz., real or hypothetical pieces of knowledge, like e.g. physical hypotheses, that are useful in assigning a probability and satisfy some additional logical properties - that are uniquely indexed by the probability distributions they lead to.<|reference_end|> | arxiv | @article{mana2006`plausibilities,
title={`Plausibilities of plausibilities': an approach through circumstances},
author={P. G. L. Porta Mana, A. M{aa}nsson, G. Bj"ork},
journal={arXiv preprint arXiv:quant-ph/0607111},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0607111},
primaryClass={quant-ph cs.AI}
} | mana2006`plausibilities |
arxiv-677375 | quant-ph/0607173 | The one-way communication complexity of the Boolean Hidden Matching Problem | <|reference_start|>The one-way communication complexity of the Boolean Hidden Matching Problem: We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for this problem, we obtain an exponential separation of quantum and classical one-way communication complexity for partial functions. A similar result was independently obtained by Gavinsky, Kempe, de Wolf [GKdW06]. Our lower bound is obtained by Fourier analysis, using the Fourier coefficients inequality of Kahn Kalai and Linial [KKL88].<|reference_end|> | arxiv | @article{kerenidis2006the,
title={The one-way communication complexity of the Boolean Hidden Matching
Problem},
author={Iordanis Kerenidis, Ran Raz},
journal={arXiv preprint arXiv:quant-ph/0607173},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0607173},
primaryClass={quant-ph cs.CC}
} | kerenidis2006the |
arxiv-677376 | quant-ph/0607174 | Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function | <|reference_start|>Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function: We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently by Kerenidis and Raz [KR06]. Our version of the result gives an example in the bounded storage model of cryptography, where the key is secure if the adversary has a certain amount of classical storage, but is completely insecure if he has a similar amount of quantum storage.<|reference_end|> | arxiv | @article{gavinsky2006exponential,
title={Exponential Separation of Quantum and Classical One-Way Communication
Complexity for a Boolean Function},
author={Dmytro Gavinsky, Julia Kempe, Ronald de Wolf},
journal={arXiv preprint arXiv:quant-ph/0607174},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0607174},
primaryClass={quant-ph cs.CC}
} | gavinsky2006exponential |
arxiv-677377 | quant-ph/0608026 | Search via Quantum Walk | <|reference_start|>Search via Quantum Walk: We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis (2004) and Szegedy (2004). Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chains. In addition, it is conceptually simple and avoids some technical difficulties in the previous analyses of several algorithms based on quantum walk.<|reference_end|> | arxiv | @article{magniez2006search,
title={Search via Quantum Walk},
author={Fr'ed'eric Magniez, Ashwin Nayak, J'er'emie Roland and Miklos
Santha},
journal={SIAM Journal on Computing, 40(1):142-164, 2011},
year={2006},
doi={10.1137/090745854},
archivePrefix={arXiv},
eprint={quant-ph/0608026},
primaryClass={quant-ph cs.CC cs.DS}
} | magniez2006search |
arxiv-677378 | quant-ph/0609028 | Secure Controlled Teleportation | <|reference_start|>Secure Controlled Teleportation: Several protocols for controlled teleportation were suggested by Yang, Chu, and Han [PRA 70, 022329 (2004)]. In these protocols, Alice teleports qubits (in an unknown state) to Bob iff a controller allows it. We view this problem in the perspective of secure multi-party quantum computation. We show that the suggested entanglement-efficient protocols for $m$-qubit controlled teleportation are open to cheating; Alice and Bob may teleport $(m-1)$-qubits of quantum information, out of the controllers' control. We conjecture that the straightforward protocol for controlled teleportation, which requires each controller to hold $m$ entangled qubits, is optimal. We prove this conjecture for a limited, but interesting, subset of protocols.<|reference_end|> | arxiv | @article{kenigsberg2006secure,
title={Secure Controlled Teleportation},
author={Dan Kenigsberg and Tal Mor},
journal={arXiv preprint arXiv:quant-ph/0609028},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0609028},
primaryClass={quant-ph cs.CR}
} | kenigsberg2006secure |
arxiv-677379 | quant-ph/0609117 | Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions | <|reference_start|>Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions: Qubit networks with long-range interactions inspired by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored memory. The maximum memory capacity p of these qubit networks is reached at a memory density p/n=1.<|reference_end|> | arxiv | @article{diamantini2006quantum,
title={Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions},
author={M.Cristina Diamantini and Carlo A. Trugenberger},
journal={arXiv preprint arXiv:quant-ph/0609117},
year={2006},
doi={10.1103/PhysRevLett.97.130503},
archivePrefix={arXiv},
eprint={quant-ph/0609117},
primaryClass={quant-ph cond-mat.dis-nn cs.NE}
} | diamantini2006quantum |
arxiv-677380 | quant-ph/0609138 | On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism | <|reference_start|>On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism: It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Omega(n log n) coset states. One of the only known models for how such a measurement could be carried out efficiently is Kuperberg's algorithm for the HSP in the dihedral group, in which quantum states are adaptively combined and measured according to the decomposition of tensor products into irreducible representations. This ``quantum sieve'' starts with coset states, and works its way down towards representations whose probabilities differ depending on, for example, whether the hidden subgroup is trivial or nontrivial. In this paper we give strong evidence that no such approach can succeed for Graph Isomorphism. Specifically, we consider the natural reduction of Graph Isomorphism to the HSP over the the wreath product S_n \wr Z_2. We show, modulo a group-theoretic conjecture regarding the asymptotic characters of the symmetric group, that no matter what rule we use to adaptively combine quantum states, there is a constant b > 0 such that no algorithm in this family can solve Graph Isomorphism in e^{b sqrt{n}} time. In particular, such algorithms are essentially no better than the best known classical algorithms, whose running time is e^{O(sqrt{n \log n})}.<|reference_end|> | arxiv | @article{moore2006on,
title={On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism},
author={Cristopher Moore and Alexander Russell},
journal={arXiv preprint arXiv:quant-ph/0609138},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0609138},
primaryClass={quant-ph cs.CC math.RT}
} | moore2006on |
arxiv-677381 | quant-ph/0609205 | Group Theoretical Formulation of Quantum Partial Search Algorithm | <|reference_start|>Group Theoretical Formulation of Quantum Partial Search Algorithm: Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster, this is partial search. An example is the following: exact address of the target item is given by a sequence of many bits, but we need to know only some of them. More generally partial search considers the following problem: a database is separated into several blocks. We want to find a block with the target item, not the target item itself. In this paper we reformulate quantum partial search algorithm in terms of group theory.<|reference_end|> | arxiv | @article{korepin2006group,
title={Group Theoretical Formulation of Quantum Partial Search Algorithm},
author={Vladimir E. Korepin and Brenno C. Vallilo},
journal={Prog. Theor. Phys. Vol. 116, No. 5 (2006), p. 783},
year={2006},
doi={10.1143/PTP.116.783},
number={YIPT-SB-06-41},
archivePrefix={arXiv},
eprint={quant-ph/0609205},
primaryClass={quant-ph cs.DS math.GR}
} | korepin2006group |
arxiv-677382 | quant-ph/0609229 | Ergodic Classical-Quantum Channels: Structure and Coding Theorems | <|reference_start|>Ergodic Classical-Quantum Channels: Structure and Coding Theorems: We consider ergodic causal classical-quantum channels (cq-channels) which additionally have a decaying input memory. In the first part we develop some structural properties of ergodic cq-channels and provide equivalent conditions for ergodicity. In the second part we prove the coding theorem with weak converse for causal ergodic cq-channels with decaying input memory. Our proof is based on the possibility to introduce joint input-output state for the cq-channels and an application of the Shannon-McMillan theorem for ergodic quantum states. In the last part of the paper it is shown how this result implies coding theorem for the classical capacity of a class of causal ergodic quantum channels.<|reference_end|> | arxiv | @article{bjelakovic2006ergodic,
title={Ergodic Classical-Quantum Channels: Structure and Coding Theorems},
author={Igor Bjelakovic, Holger Boche},
journal={IEEE Transactions on Information Theory Vol. 54, No. 2, pp.
723-742, February 2008},
year={2006},
doi={10.1109/TIT.2007.913232},
archivePrefix={arXiv},
eprint={quant-ph/0609229},
primaryClass={quant-ph cs.IT math-ph math.IT math.MP}
} | bjelakovic2006ergodic |
arxiv-677383 | quant-ph/0610153 | Subsystem Codes | <|reference_start|>Subsystem Codes: We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist [[n,n-2d+2,r>0,d]]<sub>q</sub> subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits.<|reference_end|> | arxiv | @article{aly2006subsystem,
title={Subsystem Codes},
author={Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli},
journal={arXiv preprint arXiv:quant-ph/0610153},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0610153},
primaryClass={quant-ph cs.IT math.IT}
} | aly2006subsystem |
arxiv-677384 | quant-ph/0610200 | Quantum List Decoding of Classical Block Codes of Polynomially Small Rate from Quantumly Corrupted Codewords | <|reference_start|>Quantum List Decoding of Classical Block Codes of Polynomially Small Rate from Quantumly Corrupted Codewords: Given a classical error-correcting block code, the task of quantum list decoding is to produce from any quantumly corrupted codeword a short list containing all messages whose codewords exhibit high "presence" in the quantumly corrupted codeword. Efficient quantum list decoders have been used to prove a quantum hardcore property of classical codes. However, the code rates of all known families of efficiently quantum list-decodable codes are, unfortunately, too small for other practical applications. To improve those known code rates, we prove that a specific code family of polynomially small code rate over a fixed code alphabet, obtained by concatenating generalized Reed-Solomon codes as outer codes with Hadamard codes as inner codes, has an efficient quantum list-decoding algorithm if its codewords have relatively high codeword presence in a given quantumly corrupted codeword. As an immediate application, we use the quantum list decodability of this code family to solve a certain form of quantum search problems in polynomial time. When the codeword presence becomes smaller, in contrast, we show that the quantum list decodability of generalized Reed-Solomon codes with high confidence is closely related to the efficient solvability of the following two problems: the noisy polynomial interpolation problem and the bounded distance vector problem. Moreover, assuming that NP is not included in BQP, we also prove that no efficient quantum list decoder exists for the generalized Reed-Solomon codes.<|reference_end|> | arxiv | @article{yamakami2006quantum,
title={Quantum List Decoding of Classical Block Codes of Polynomially Small
Rate from Quantumly Corrupted Codewords},
author={Tomoyuki Yamakami},
journal={Baltic Journal of Modern Computing, Vol. 4 (2016), No. 4, pp.
753-788},
year={2006},
doi={10.22364/bjmc.2016.4.4},
archivePrefix={arXiv},
eprint={quant-ph/0610200},
primaryClass={quant-ph cs.CC cs.IT math.IT}
} | yamakami2006quantum |
arxiv-677385 | quant-ph/0611021 | Merlin-Arthur Games and Stoquastic Complexity | <|reference_start|>Merlin-Arthur Games and Stoquastic Complexity: MA is a class of decision problems for which `yes'-instances have a proof that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem which we call the stoquastic k-SAT problem. This is a matrix-valued analogue of the satisfiability problem in which clauses are k-qubit projectors with non-negative matrix elements, while a satisfying assignment is a vector that belongs to the space spanned by these projectors. Stoquastic k-SAT is the first non-trivial example of a MA-complete problem. We also study the minimum eigenvalue problem for local stoquastic Hamiltonians that was introduced in quant-ph/0606140, stoquastic LH-MIN. A new complexity class StoqMA is introduced so that stoquastic LH-MIN is StoqMA-complete. Lastly, we consider the average LH-MIN problem for local stoquastic Hamiltonians that depend on a random or `quenched disorder' parameter, stoquastic AV-LH-MIN. We prove that stoquastic AV-LH-MIN is contained in the complexity class \AM, the class of decision problems for which yes-instances have a randomized interactive proof with two-way communication between prover and verifier.<|reference_end|> | arxiv | @article{bravyi2006merlin-arthur,
title={Merlin-Arthur Games and Stoquastic Complexity},
author={Sergey Bravyi, Arvid J. Bessen, and Barbara M. Terhal},
journal={arXiv preprint arXiv:quant-ph/0611021},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0611021},
primaryClass={quant-ph cs.CC}
} | bravyi2006merlin-arthur |
arxiv-677386 | quant-ph/0611033 | Approximate Randomization of Quantum States With Fewer Bits of Key | <|reference_start|>Approximate Randomization of Quantum States With Fewer Bits of Key: Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.<|reference_end|> | arxiv | @article{dickinson2006approximate,
title={Approximate Randomization of Quantum States With Fewer Bits of Key},
author={Paul A. Dickinson (1) and Ashwin Nayak (1,2) ((1) C&O and IQC, U.
Waterloo, (2) Perimeter Institute)},
journal={arXiv preprint arXiv:quant-ph/0611033},
year={2006},
doi={10.1063/1.2400876},
archivePrefix={arXiv},
eprint={quant-ph/0611033},
primaryClass={quant-ph cs.CR}
} | dickinson2006approximate |
arxiv-677387 | quant-ph/0611167 | Continuous Variable Quantum Cryptography using Two-Way Quantum Communication | <|reference_start|>Continuous Variable Quantum Cryptography using Two-Way Quantum Communication: Quantum cryptography has been recently extended to continuous variable systems, e.g., the bosonic modes of the electromagnetic field. In particular, several cryptographic protocols have been proposed and experimentally implemented using bosonic modes with Gaussian statistics. Such protocols have shown the possibility of reaching very high secret-key rates, even in the presence of strong losses in the quantum communication channel. Despite this robustness to loss, their security can be affected by more general attacks where extra Gaussian noise is introduced by the eavesdropper. In this general scenario we show a "hardware solution" for enhancing the security thresholds of these protocols. This is possible by extending them to a two-way quantum communication where subsequent uses of the quantum channel are suitably combined. In the resulting two-way schemes, one of the honest parties assists the secret encoding of the other with the chance of a non-trivial superadditive enhancement of the security thresholds. Such results enable the extension of quantum cryptography to more complex quantum communications.<|reference_end|> | arxiv | @article{pirandola2006continuous,
title={Continuous Variable Quantum Cryptography using Two-Way Quantum
Communication},
author={Stefano Pirandola, Stefano Mancini, Seth Lloyd, and Samuel L.
Braunstein},
journal={Nature Physics 4, 726 - 730 (2008)},
year={2006},
doi={10.1038/nphys1018},
archivePrefix={arXiv},
eprint={quant-ph/0611167},
primaryClass={quant-ph cs.CR cs.IT math.IT physics.optics}
} | pirandola2006continuous |
arxiv-677388 | quant-ph/0611234 | Toward a general theory of quantum games | <|reference_start|>Toward a general theory of quantum games: We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamio{\l}kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaev's lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.<|reference_end|> | arxiv | @article{gutoski2006toward,
title={Toward a general theory of quantum games},
author={Gus Gutoski and John Watrous},
journal={Proceedings of STOC 2007, pages 565-574},
year={2006},
doi={10.1145/1250790.1250873},
archivePrefix={arXiv},
eprint={quant-ph/0611234},
primaryClass={quant-ph cs.CC cs.GT}
} | gutoski2006toward |
arxiv-677389 | quant-ph/0612014 | A Tight High-Order Entropic Quantum Uncertainty Relation With Applications | <|reference_start|>A Tight High-Order Entropic Quantum Uncertainty Relation With Applications: We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded quantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.<|reference_end|> | arxiv | @article{damgaard2006a,
title={A Tight High-Order Entropic Quantum Uncertainty Relation With
Applications},
author={Ivan B. Damgaard, Serge Fehr, Renato Renner, Louis Salvail, Christian
Schaffner},
journal={full version of CRYPTO 2007, LNCS 4622},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0612014},
primaryClass={quant-ph cs.CR}
} | damgaard2006a |
arxiv-677390 | quant-ph/0612052 | Deciding whether a quantum state has secret correlations is an NP-complete problem | <|reference_start|>Deciding whether a quantum state has secret correlations is an NP-complete problem: From the NP-hardness of the quantum separability problem and the relation between bipartite entanglement and the secret key correlations, it is shown that the problem deciding whether a given quantum state has secret correlations in it or not is in NP-complete.<|reference_end|> | arxiv | @article{lee2006deciding,
title={Deciding whether a quantum state has secret correlations is an
NP-complete problem},
author={Jae-Weon Lee, DoYong Kwon, Jaewan Kim},
journal={arXiv preprint arXiv:quant-ph/0612052},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0612052},
primaryClass={quant-ph cs.IT math.IT}
} | lee2006deciding |
arxiv-677391 | quant-ph/0612107 | How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden Subgroup Problem | <|reference_start|>How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden Subgroup Problem: It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was discovered within the framework of using pretty-good measurements for obtaining optimal measurements in the hidden subgroup problem. Here we show how to solve the Heisenberg hidden subgroup problem using arguments based instead on the symmetry of certain hidden subgroup states. The symmetry we consider leads naturally to a unitary transform known as the Clebsch-Gordan transform over the Heisenberg group. This gives a new representation theoretic explanation for the pretty-good measurement derived algorithm for efficiently solving the Heisenberg hidden subgroup problem and provides evidence that Clebsch-Gordan transforms over finite groups are a new primitive in quantum algorithm design.<|reference_end|> | arxiv | @article{bacon2006how,
title={How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden
Subgroup Problem},
author={Dave Bacon},
journal={arXiv preprint arXiv:quant-ph/0612107},
year={2006},
archivePrefix={arXiv},
eprint={quant-ph/0612107},
primaryClass={quant-ph cs.CC}
} | bacon2006how |
arxiv-677392 | quant-ph/0612155 | A father protocol for quantum broadcast channels | <|reference_start|>A father protocol for quantum broadcast channels: A new protocol for quantum broadcast channels based on the fully quantum Slepian-Wolf protocol is presented. The protocol yields an achievable rate region for entanglement-assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Marton's region for classical broadcast channels. The protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement-assisted classical communication; in the case of unassisted transmission, the region we obtain has no independent constraint on the sum rate, only on the individual transmission rates. Regularized versions of all three rate regions are provably optimal.<|reference_end|> | arxiv | @article{dupuis2006a,
title={A father protocol for quantum broadcast channels},
author={Fr'ed'eric Dupuis, Patrick Hayden, Ke Li},
journal={IEEE Transactions on Information Theory 56(6)2946-2956, 2010},
year={2006},
doi={10.1109/TIT.2010.2046217},
archivePrefix={arXiv},
eprint={quant-ph/0612155},
primaryClass={quant-ph cs.IT math.IT}
} | dupuis2006a |
arxiv-677393 | quant-ph/0612199 | Lineal: A linear-algebraic Lambda-calculus | <|reference_start|>Lineal: A linear-algebraic Lambda-calculus: We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus with the possibility to make arbitrary linear combinations of terms alpha.t + beta.u. We describe how to "execute" this language in terms of a few rewrite rules, and justify them through the two fundamental requirements that the language be a language of linear operators, and that it be higher-order. We mention the perspectives of this work in the field of quantum computation, whose circuits we show can be easily encoded in the calculus. Finally, we prove the confluence of the entire calculus.<|reference_end|> | arxiv | @article{arrighi2006lineal:,
title={Lineal: A linear-algebraic Lambda-calculus},
author={Pablo Arrighi, Gilles Dowek},
journal={Logical Methods in Computer Science, Volume 13, Issue 1 (March 17,
2017) lmcs:3203},
year={2006},
doi={10.23638/LMCS-13(1:8)2017},
archivePrefix={arXiv},
eprint={quant-ph/0612199},
primaryClass={quant-ph cs.LO cs.PL}
} | arrighi2006lineal: |
arxiv-677394 | quant-ph/0701020 | Quantum Quasi-Cyclic LDPC Codes | <|reference_start|>Quantum Quasi-Cyclic LDPC Codes: In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our proposed codes have lots of variations for length, code rate. These codes are obtained by a descrete mathematical characterization for model matrices of quasi-cyclic LDPC codes. Our proposed codes achieve a bounded distance decoding (BDD) bound, or known as VG bound, and achieve a lower bound of the code length.<|reference_end|> | arxiv | @article{hagiwara2007quantum,
title={Quantum Quasi-Cyclic LDPC Codes},
author={Manabu Hagiwara, Hideki Imai},
journal={arXiv preprint arXiv:quant-ph/0701020},
year={2007},
doi={10.1109/ISIT.2007.4557323},
archivePrefix={arXiv},
eprint={quant-ph/0701020},
primaryClass={quant-ph cs.IT math-ph math.CO math.IT math.MP}
} | hagiwara2007quantum |
arxiv-677395 | quant-ph/0701037 | Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller Codes | <|reference_start|>Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller Codes: Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional codes are derived from generalized Reed-Solomon codes and from Reed- Muller codes. A Singleton bound for pure convolutional stabilizer codes is given.<|reference_end|> | arxiv | @article{aly2007quantum,
title={Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller
Codes},
author={Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli},
journal={arXiv preprint arXiv:quant-ph/0701037},
year={2007},
archivePrefix={arXiv},
eprint={quant-ph/0701037},
primaryClass={quant-ph cs.IT math.IT}
} | aly2007quantum |
arxiv-677396 | quant-ph/0701113 | A presentation of Quantum Logic based on an "and then" connective | <|reference_start|>A presentation of Quantum Logic based on an "and then" connective: When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the "and then" operation that combines old and new information. The "and then" connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the "and then" connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch (1969) satisfies all the properties studied in this paper. All properties satisfied by Finch's operation in modular lattices are valid in Hilbert Space Quantum Logic. It is not known whether all properties of Hilbert Space Quantum Logic are satisfied by Finch's operation in modular lattices. Non-commutative, non-associative algebraic structures generalizing Boolean algebras are defined, ideals are characterized and a homomorphism theorem is proved.<|reference_end|> | arxiv | @article{lehmann2007a,
title={A presentation of Quantum Logic based on an "and then" connective},
author={Daniel Lehmann},
journal={Journal of Logic and Computation 18 (1): 59-76 Feb. 2008},
year={2007},
doi={10.1093/logcom/exm054},
number={Short version in Leibniz Center, School of Engineering, Hebrew U.
TR-2007-1},
archivePrefix={arXiv},
eprint={quant-ph/0701113},
primaryClass={quant-ph cs.LO math.LO}
} | lehmann2007a |
arxiv-677397 | quant-ph/0701168 | Using quantum key distribution for cryptographic purposes: a survey | <|reference_start|>Using quantum key distribution for cryptographic purposes: a survey: The appealing feature of quantum key distribution (QKD), from a cryptographic viewpoint, is the ability to prove the information-theoretic security (ITS) of the established keys. As a key establishment primitive, QKD however does not provide a standalone security service in its own: the secret keys established by QKD are in general then used by a subsequent cryptographic applications for which the requirements, the context of use and the security properties can vary. It is therefore important, in the perspective of integrating QKD in security infrastructures, to analyze how QKD can be combined with other cryptographic primitives. The purpose of this survey article, which is mostly centered on European research results, is to contribute to such an analysis. We first review and compare the properties of the existing key establishment techniques, QKD being one of them. We then study more specifically two generic scenarios related to the practical use of QKD in cryptographic infrastructures: 1) using QKD as a key renewal technique for a symmetric cipher over a point-to-point link; 2) using QKD in a network containing many users with the objective of offering any-to-any key establishment service. We discuss the constraints as well as the potential interest of using QKD in these contexts. We finally give an overview of challenges relative to the development of QKD technology that also constitute potential avenues for cryptographic research.<|reference_end|> | arxiv | @article{alléaume2007using,
title={Using quantum key distribution for cryptographic purposes: a survey},
author={Romain All'eaume, Cyril Branciard, Jan Bouda, Thierry Debuisschert,
Mehrdad Dianati, Nicolas Gisin, Mark Godfrey, Philippe Grangier, Thomas
Langer, Norbert Lutkenhaus, Christian Monyk, Philippe Painchault, Momtchil
Peev, Andreas Poppe, Thomas Pornin, John Rarity, Renato Renner, Gregoire
Ribordy, Michel Riguidel, Louis Salvail, Andrew Shields, Harald Weinfurter,
Anton Zeilinger},
journal={Theoretical Computer Science, 560 (2014), pp. 62-81},
year={2007},
archivePrefix={arXiv},
eprint={quant-ph/0701168},
primaryClass={quant-ph cs.CR cs.IT math.IT}
} | alléaume2007using |
arxiv-677398 | quant-ph/0701171 | Turning the Liar paradox into a metatheorem of Basic logic | <|reference_start|>Turning the Liar paradox into a metatheorem of Basic logic: We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence loses its own identity. This prevents having self-referential paradoxes in the corresponding metalanguage. In this context, we introduce a generalized definition of self-reference, which is needed to deal with the multiplicative connectives of substructural logics.<|reference_end|> | arxiv | @article{zizzi2007turning,
title={Turning the Liar paradox into a metatheorem of Basic logic},
author={Paola A. Zizzi},
journal={arXiv preprint arXiv:quant-ph/0701171},
year={2007},
archivePrefix={arXiv},
eprint={quant-ph/0701171},
primaryClass={quant-ph cs.LO math.LO}
} | zizzi2007turning |
arxiv-677399 | quant-ph/0702005 | A decoupling approach to the quantum capacity | <|reference_start|>A decoupling approach to the quantum capacity: We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will with high probability be decoupled from the channel's environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modification yielding unitarily invariant ensembles of maximally entangled codes.<|reference_end|> | arxiv | @article{hayden2007a,
title={A decoupling approach to the quantum capacity},
author={Patrick Hayden, Michal Horodecki, Andreas Winter and Jon Yard},
journal={Open Syst. Inf. Dyn. 15 (2008) 7-19},
year={2007},
doi={10.1142/S1230161208000043},
archivePrefix={arXiv},
eprint={quant-ph/0702005},
primaryClass={quant-ph cs.IT math.IT}
} | hayden2007a |
arxiv-677400 | quant-ph/0702072 | Markovian Entanglement Networks | <|reference_start|>Markovian Entanglement Networks: Graphical models of probabilistic dependencies have been extensively investigated in the context of classical uncertainty. However, in some domains (most notably, in computational physics and quantum computing) the nature of the relevant uncertainty is non-classical, and the laws of classical probability theory are superseded by those of quantum mechanics. In this paper we introduce Markovian Entanglement Networks (MEN), a novel class of graphical representations of quantum-mechanical dependencies in the context of such non-classical systems. MEN are the quantum-mechanical analogue of Markovian Networks, a family of undirected graphical representations which, in the classical domain, exploit a notion of conditional independence among subsystems. After defining a notion of conditional independence appropriate to our domain (conditional separability), we prove that the conditional separabilities induced by a quantum-mechanical wave function are effectively reflected in the graphical structure of MEN. Specifically, we show that for any wave function there exists a MEN which is a perfect map of its conditional separabilities. Next, we show how the graphical structure of MEN can be used to effectively classify the pure states of three-qubit systems. We also demonstrate that, in large systems, exploiting conditional independencies may dramatically reduce the computational burden of various inference tasks. In principle, the graph-theoretic representation of conditional independencies afforded by MEN may not only facilitate the classical simulation of quantum systems, but also provide a guide to the efficient design and complexity analysis of quantum algorithms and circuits.<|reference_end|> | arxiv | @article{la mura2007markovian,
title={Markovian Entanglement Networks},
author={Pierfrancesco La Mura and Lukasz Swiatczak},
journal={arXiv preprint arXiv:quant-ph/0702072},
year={2007},
number={HHL-77},
archivePrefix={arXiv},
eprint={quant-ph/0702072},
primaryClass={quant-ph cs.AI}
} | la mura2007markovian |
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