Non-Interactive Quantum Statistical and Perfect Zero-Knowledge
<|reference_start|>Non-Interactive Quantum Statistical and Perfect Zero-Knowledge: This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of non-interactive quantum perfect and statistical zero-knowledge. It is also shown that, with sharing EPR pairs a priori, the class of languages having one-sided bounded error non-interactive quantum perfect zero-knowledge proof systems has a natural complete problem. Non-triviality of such a proof system is based on the fact proved in this paper that the Graph Non-Automorphism problem, which is not known in BQP, can be reduced to our complete problem. Our results may be the first non-trivial quantum zero-knowledge proofs secure even against dishonest quantum verifiers, since our protocols are non-interactive, and thus the zero-knowledge property does not depend on whether the verifier in the protocol is honest or not. A restricted version of our complete problem derives a natural complete problem for BQP.<|reference_end|>
@article{kobayashi2002non-interactive,
    title={Non-Interactive Quantum Statistical and Perfect Zero-Knowledge},
    author={Hirotada Kobayashi},
    journal={arXiv preprint arXiv:quant-ph/0207158},
    year={2002},
    archivePrefix={arXiv},
    eprint={quant-ph/0207158},
    primaryClass={quant-ph cs.CC}
}