We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing protocols in the relativistic setting which satisfy a weaker variant of the special soundness property due to Unruh (EUROCRYPT 2012). We show that there exists quantum proofs of knowledge with knowledge error 1/2 + negl({\eta}) for all relations in NP via a construction of such a system for the Hamiltonian cycle relation using a general relativistic commitment scheme exhibiting the fairly-binding property due to Fehr and Fillinger (EUROCRYPT 2016). We further show that one can construct quantum proof of knowledge extractors for proof systems which do not exhibit special soundness, and therefore require an extractor to rewind multiple times. We develop a new multi-prover quantum rewinding technique by combining ideas from monogamy of entanglement and gentle measurement lemmas that can break the quantum rewinding barrier. Finally, we prove a new bound on the impact of consecutive measurements and use it to significantly improve the soundness bound of some existing relativistic zero knowledge proof systems, such as the one due to Chailloux and Leverrier (EUROCRYPT 2017).

翻译：我们首次研究了基于经典通信的相对论零知识量子知识证明系统，形式化定义了一系列重要概念，并为所有满足Unruh（EUROCRYPT 2012）提出的弱化版特殊可靠性属性的现有相对论协议构建了相应的知识提取器。通过利用Fehr和Fillinger（EUROCRYPT 2016）提出的具有公平约束性的一般相对论承诺方案，我们针对哈密顿回路关系构建了此类系统，证明对于所有NP关系均存在知识误差为1/2 + negl(η)的量子知识证明。进一步地，我们展示了如何为不具备特殊可靠性的证明系统构建量子知识证明提取器，这类系统需要提取器进行多次回卷操作。通过结合量子纠缠单配性与温和测量引理的思想，我们开发了一种新型多证明者量子回卷技术，能够突破量子回卷的固有屏障。最后，我们证明了连续测量影响的新界限，并利用该结果显著改进了现有相对论零知识证明系统（如Chailloux和Leverrier在EUROCRYPT 2017提出的方案）的可靠性界限。