Foundational results in theoretical computer science have established that everything provable, is provable in zero knowledge. However, this assertion fundamentally assumes a classical interpretation of computation and many interesting physical statements that one can hope to prove are not characterized. In this work, we consider decision problems, where the problem instance itself is specified by a (pure) quantum state. We discuss several motivating examples for this notion and, as our main technical result, we show that every quantum problem that is provable with an interactive protocol, is also provable in zero-knowledge. Our protocol achieves unconditional soundness and computational zero-knowledge, under standard assumptions in cryptography. In addition, we show how our techniques yield a protocol for the Uhlmann transformation problem that achieves a meaningful notion of zero-knowledge, also in the presence of a malicious verifier.

翻译：理论计算机科学的基础性成果已证明，所有可证明的命题皆可在零知识条件下被证明。然而，这一论断从根本上假定了经典计算范式，且未能刻画许多有望被证明的有趣物理命题。在本研究中，我们考察一类决策问题，其问题实例本身由（纯）量子态所描述。我们讨论了该概念的若干激励性示例，并作为核心技术成果，证明了所有可通过交互式协议证明的量子问题同样可在零知识条件下被证明。该协议在密码学标准假设下实现了无条件可靠性与计算性零知识。此外，我们展示了如何利用该技术为乌尔曼变换问题构建协议，该协议即使在恶意验证者存在时仍能实现具有实质意义的零知识特性。