Quantum Oracle Interrogation: Getting all information for almost half the price
<|reference_start|>Quantum Oracle Interrogation: Getting all information for almost half the price: Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+sqrt(N) queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(sqrt(N)) oracle queries.   In the second part of the article `approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.<|reference_end|>
@article{van dam1998quantum,
    title={Quantum Oracle Interrogation: Getting all information for almost half
  the price},
    author={Wim van Dam (U of Oxford, CWI)},
    journal={Proceedings of the 39th Annual IEEE Symposium on Foundations of
  Computer Science (FOCS), pages 362-367 (1998)},
    year={1998},
    doi={10.1109/SFCS.1998.743486},
    number={CQC-040598},
    archivePrefix={arXiv},
    eprint={quant-ph/9805006},
    primaryClass={quant-ph cs.CC}
}