论文标题
量子知识的经典证明
Classical proofs of quantum knowledge
论文作者
论文摘要
我们在验证者是经典的环境中定义了知识证明的概念，但供者是量子，以及证人所持的证人通常是量子状态。我们建立了我们定义的简单属性，包括，如果某种状态存在无损的经典量子知识证明，那么该状态可以由无限的对手克隆，并且在我们定义中的某些条件下，在我们定义中的某些条件下，可以用作难以克隆的状态的知识证明协议，以作为（破坏性）量子验证协议。此外，我们还提供了两个协议的示例（均受量子货币计划的私钥经典验证协议的启发），我们可以证明在我们的定义下是量子知识的证明。在这样做时，我们介绍了对此类协议进行分析的技术，这些方案是基于非本地游戏文献所产生的。最后，我们表明，根据我们的定义，Mahadev（FOCS 2018）引入的验证协议是QMA关系的量子知识的经典论点。在所有情况下，我们构建了一个明确的量子提取器，该提取器能够产生量子证人，即给出了对摊子的黑盒量子（倒带）访问权限，后者包括能够连贯地执行从Verifier的消息叠加控制的摊子的黑盒电路。
We define the notion of a proof of knowledge in the setting where the verifier is classical, but the prover is quantum, and where the witness that the prover holds is in general a quantum state. We establish simple properties of our definition, including that, if a nondestructive classical proof of quantum knowledge exists for some state, then that state can be cloned by an unbounded adversary, and that, under certain conditions on the parameters in our definition, a proof of knowledge protocol for a hard-to-clone state can be used as a (destructive) quantum money verification protocol. In addition, we provide two examples of protocols (both inspired by private-key classical verification protocols for quantum money schemes) which we can show to be proofs of quantum knowledge under our definition. In so doing, we introduce techniques for the analysis of such protocols which build on results from the literature on nonlocal games. Finally, we show that, under our definition, the verification protocol introduced by Mahadev (FOCS 2018) is a classical argument of quantum knowledge for QMA relations. In all cases, we construct an explicit quantum extractor that is able to produce a quantum witness given black-box quantum (rewinding) access to the prover, the latter of which includes the ability to coherently execute the prover's black-box circuit controlled on a superposition of messages from the verifier.
