MoMPy：面向半定规划松弛的矩矩阵自动构建工具
MoMPy: automated construction of moment matrices for semidefinite programming relaxations
AI总结：
MoMPy是开源Python工具，可自动为SDP层次结构构建矩矩阵，核心抽象与物理场景无关，经多任务验证且在8种场景中完成基准测试，支持多种量子相关任务的SDP建模。
AI中文摘要：
我们提出了MoMPy，这是一个开源Python软件包，可对半定规划（SDP）层次结构的矩矩阵提供统一的声明式构建方式。用户声明算子标签以及少量结构关系，MoMPy会返回一个包含SDP变量索引的矩阵，其中所有隐含的标识都已完成，可直接用于CVXPY或其他建模层。在内部，标识问题被重新表述为整数元组上的单词重写问题，通过带记忆的广度优先闭包结合不相交集森林求解，因此每个不同的单项式在每次构建中仅被处理一次，无论其最终标记多少个矩阵元素。核心抽象与物理场景无关：同一构建方式可处理迹型、态（NPA）及块值矩，不涉及参与方、设置或制备的概念。我们在三方Mermin不等式、两方CHSH不等式、引导场景中的测量兼容性、制备-测量场景中的态区分与维度见证、设备无关随机数认证以及已知系综的确定性相关性认证等任务上展示了该方法的通用性。该构建方式已通过独立的暴力实现验证，并在8种结构不同的场景中进行了基准测试，涵盖两方和三方贝尔测试、异质结果、引导型、联合可测量及网络配置。
英文摘要：
We present MoMPy, an open-source Python package that provides a unified, declarative construction of moment matrices for semidefinite programming (SDP) hierarchies. The user declares operator labels together with a small set of structural relations, and MoMPy returns a matrix of SDP variable indices in which every implied identification has already been made, ready for CVXPY or any other modelling layer. Internally, the identification problem is recast as a word-rewriting problem on tuples of integers and solved with a memoised breadth-first closure coupled to a disjoint-set forest, so that each distinct monomial is processed exactly once per build, however many matrix entries it eventually labels. The central abstraction is independent of the physical scenario: the same construction handles tracial, state (NPA), and block-valued moments, with no notion of parties, settings or preparations. We demonstrate this generality on a tripartite Mermin inequality, the bipartite CHSH inequality, measurement compatibility in a steering scenario, state discrimination and dimension witnessing in prepare-and-measure scenarios, device-independent randomness certification, and certification of deterministic correlations from known ensembles. The construction is validated against an independent brute-force implementation and benchmarked across eight structurally distinct scenarios, spanning bipartite and tripartite Bell tests, heterogeneous-outcome, steering-type, jointly-measurable and network configurations.
