标题： 通过顺序NPA层次结构的双部分编译贝尔游戏的定量量子安全性 显示英文标题

标题： Quantitative Quantum Soundness for Bipartite Compiled Bell Games via the Sequential NPA Hierarchy

摘要： 在密码学假设下编译贝尔游戏取代了物理隔离的需要，使得可以使用单个不可信设备探测非定域性。 虽然Kalai等人（STOC'23）表明这种编译保留了量子优势，但其定量量子可靠性仍是一个开放问题。 我们通过两个主要贡献来解决这一差距。 首先，我们建立了每个二元编译贝尔游戏的首个定量量子可靠性界限，其最优量子策略是有限维的：任何多项式时间证明者的得分在编译游戏中与游戏的理想量子值几乎无法区分。 更一般地，对于所有二元游戏，我们证明编译得分不能显著超过由新形式化的顺序Navascués-Pironio-Acín（NPA）层次结构给出的界限。 其次，我们提供了这一顺序NPA层次结构的完整表征，将其确立为一个稳健的数值工具，具有独立的兴趣。 最后，对于没有有限维最优策略的游戏，我们探讨了NPA近似误差在定量界定其编译得分中的必要性，将这些考虑与复杂性猜想$\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$以及诸如“弱交换”量子寄存器的量子同态加密正确性等开放挑战联系起来。 显示英文摘要

摘要： Compiling Bell games under cryptographic assumptions replaces the need for physical separation, allowing nonlocality to be probed with a single untrusted device. While Kalai et al. (STOC'23) showed that this compilation preserves quantum advantages, its quantitative quantum soundness has remained an open problem. We address this gap with two primary contributions. First, we establish the first quantitative quantum soundness bounds for every bipartite compiled Bell game whose optimal quantum strategy is finite-dimensional: any polynomial-time prover's score in the compiled game is negligibly close to the game's ideal quantum value. More generally, for all bipartite games we show that the compiled score cannot significantly exceed the bounds given by a newly formalized sequential Navascu\'es-Pironio-Ac\'in (NPA) hierarchy. Second, we provide a full characterization of this sequential NPA hierarchy, establishing it as a robust numerical tool that is of independent interest. Finally, for games without finite-dimensional optimal strategies, we explore the necessity of NPA approximation error for quantitatively bounding their compiled scores, linking these considerations to the complexity conjecture $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$ and open challenges such as quantum homomorphic encryption correctness for "weakly commuting" quantum registers.