标题： 所有多部分编译非局部游戏的渐近量子值的界 显示英文标题

标题： Bounding the asymptotic quantum value of all multipartite compiled non-local games

摘要： 非局部博弈是区分经典世界和量子世界中可能的相关性的强大工具。 Kalai 等人（STOC'23）提出了一种编译器，该编译器将多部分非局部博弈转换为具有单个证明者的交互协议，依赖于密码学工具来消除玩家物理分离的假设。 虽然该构造的量子完备性和经典合理性已针对所有多部分博弈得到确立，但量子合理性仅在二部分博弈的特殊情况下已知。 在本文中，我们证明 Kalai 等人的编译器确实实现了所有多部分编译非局部博弈的量子合理性，通过证明在渐近情况下可以生成的任何相关性都对应于量子对 commuting 策略。 我们的证明使用了算子代数理论中的技术，并依赖于在多部分情况下将顺序操作无信号策略表征为量子 commuting 算子策略，从而推广了几项先前的结果。 在此过程中，我们构建了顺序 PVM 的通用 C*-代数，并证明了 C*-代数上完全正映射的 Radon-Nikodym 导数的新链式规则，这可能具有独立的兴趣。 显示英文摘要

摘要： Non-local games are a powerful tool to distinguish between correlations possible in classical and quantum worlds. Kalai et al. (STOC'23) proposed a compiler that converts multipartite non-local games into interactive protocols with a single prover, relying on cryptographic tools to remove the assumption of physical separation of the players. While quantum completeness and classical soundness of the construction have been established for all multipartite games, quantum soundness is known only in the special case of bipartite games. In this paper, we prove that the Kalai et al.'s compiler indeed achieves quantum soundness for all multipartite compiled non-local games, by showing that any correlations that can be generated in the asymptotic case correspond to quantum commuting strategies. Our proof uses techniques from the theory of operator algebras, and relies on a characterisation of sequential operationally no-signalling strategies as quantum commuting operator strategies in the multipartite case, thereby generalising several previous results. On the way, we construct universal C*-algebras of sequential PVMs and prove a new chain rule for Radon-Nikodym derivatives of completely positive maps on C*-algebras which may be of independent interest.