A cryptographic compiler introduced by Kalai et al. (STOC'23) converts any nonlocal game into an interactive protocol with a single computationally bounded prover. Although the compiler is known to be sound in the case of classical provers and complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game. Our result employs techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. It further relies on a sequential characterization of quantum commuting operator correlations which may be of independent interest.

翻译：Kalai等人（STOC'23）提出的密码学编译器可将任意非局域博弈转化为与单个计算受限证明者的交互协议。虽然已知该编译器在经典证明者情况下具有可靠性，在量子情况下具有完备性，但迄今为止量子可靠性仅针对特定博弈类别得以建立。本研究为所有编译型双参与者非局域博弈建立了量子可靠性结果。特别地，我们证明了底层非局域博弈的量子交换算子值构成编译博弈量子值的上界。本成果运用算子代数技术于计算与密码学场景，在安全参数的渐近极限中建立信息论对象，并依赖于量子交换算子关联的序列化表征方法，该方法可能具有独立学术价值。