Abstract
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 complexity class resulting from non-interactive quantum perfect zero-knowledge proof systems of perfect completeness has a natural complete promise problem. Using our complete promise problem, the Graph Non-Automorphism problem is shown to have a non-interactive quantum perfect zero-knowledge proof system.
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