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).

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