对称性分辨的树张量网络分析：辅助辅助被动线性光学中的贝尔态判别
Symmetry-resolved tree tensor network analysis of Bell-state discrimination with ancilla-assisted passive linear optics
- Banaras Hindu University（贝拿勒斯印度教大学）
- Keio University（庆应义塾大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种光子数分辨的树张量网络方法，用于高效评估辅助辅助被动线性光学贝尔态判别中的探测器支持，并推导了对称辅助资源的精确组合关系，验证了多达32个光学模式的结果。
AI中文摘要：
辅助光子允许被动线性光学贝尔态判别超越仅使用真空辅助模式时二分之一成功概率的极限。对于固定的分析器和辅助资源，判别概率由每个贝尔输入唯一出现的光子计数模式决定。我们开发了一种光子数分辨的树张量网络方法，用于评估递归结构分析器中的这些探测器支持。光子数守恒和模式对称性在检查剩余探测器支持之前将大多数贝尔态输出分离。我们建立了一种基于树张量网络的构造来评估剩余支持，无需分别回忆所有相关的光子探测器模式。我们将该方法应用于递归、乘积和不对称辅助态，最多包含32个光学模式，并复现了已知的解析和文献基准。对于在分析器两半中具有固定光子数且具有我们分析中使用的对称性的因子化辅助资源，我们还推导了一个精确的组合关系；对于反射的不对称配对，成功概率是对应对称配置的算术平均值。对较小系统的完整枚举、基于永久式的振幅计算和独立评估为数值结果提供了额外检查。
英文摘要：
Ancillary photons allow passive linear-optical Bell-state discrimination to exceed the one-half probability of success limit achievable with vacuum auxiliary modes. For a fixed analyzer and ancillary resource, the discrimination probability is determined by the photon-counting patterns that occur uniquely for each Bell input. We develop a photon-number-resolved tree tensor network method for evaluating these detector supports in recursively structured analyzers. Photon-number conservation and mode symmetries separate most of the Bell-state outputs before the remaining detector support is examined. We establish a tree tensor network based construction to evaluate the remaining support without need of recalling all relevant photon detector patterns separately. We apply the method to recursive, product, and asymmetric ancillary states with up to $32$ optical modes and reproduce known analytical and literature benchmarks. For factorized ancillary resources with fixed photon numbers in halves of the analyzer and the symmetry property used in our analysis, we also derive an exact composition relation; for reflected asymmetric pairings the success probability is the arithmetic mean of the corresponding symmetric configurations. The complete enumeration for smaller systems, permanent-based amplitude calculations, and independent evaluations provide additional checks of the numerical results.
