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|>
@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}
}