发表机构
Inria, ENS de Lyon, UCBL, LIP; Astronomical Institute, Slovak Academy of Sciences（法国国家信息与自动化研究所、里昂高等师范学院、里昂第一大学、计算与图像实验室; 斯洛伐克科学院天文研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种自动搜索高度情境性Kochen-Specker证明的方法，通过枚举反对易图并关联超文法，在无需量子比特参考的情况下高效找到最优配置，达到误差0.707，超越先前记录，并揭示线图与完美匹配的无限族结构。
AI 中文摘要
基于可观测量的Kochen-Specker证明是多量子比特泡利可观测量配置，这些可观测量被分组为上下文，其乘积为正或负单位矩阵。它们作为与状态无关的上下文性测试的鲁棒性可以通过每个上下文容忍误差$\varepsilon = 2d/|H|$来衡量，其中$d$是上下文性度，$|H|$是上下文数量。由于该度仅依赖于一个称为超文法（即由上下文超图和反对易图组成的对）的底层抽象结构，因此对高度情境性证明的搜索可以在这些结构上进行，而无需参考量子比特或任何特定的泡利标记。我们进一步利用这一点，首先枚举反对易图，然后为每个图$G$关联携带其整个超图支撑$HS(G)$的单个超文法，这样每个图仅检查一个候选。应用于House of Graphs数据库和最多24个顶点的顶点传递图普查，该流程恢复了Peres-Mermin正方形、doyly和Mermin五角星，并产生达到$\varepsilon = 0.707$的配置，而先前公布记录为$0.424$。最佳配置主要来自线图和图的并集；我们通过证明图的每个完美匹配都是其线图的上下文来解释前者，这展示了Peres-Mermin正方形和doyly作为两个无限族的首批成员。我们以辛极空间内最显著配置的有限几何描述结束，以卵形线、双曲二次曲面和Fano平面为术语。
英文摘要
Observable-based Kochen-Specker proofs are configurations of multi-qubit Pauli observables grouped into contexts whose products are plus or minus the indentity. Their robustness as state-independent contextuality tests can be measured by the tolerated error per context $\varepsilon = 2d/|H|$, where $d$ is the contextuality degree and $|H|$ the number of contexts. Since the degree depends only on an underlying abstract structure called the hypergram i.e. the pair formed by the context hypergraph and the anticommutation graph, the search for highly contextual proofs can be carried out on them instead, with no reference to qubits or to any particular Pauli labeling. We further exploit this by enumerating anticommutation graphs first, and then by associating to each graph $G$ the single hypergram carrying its entire hypergraph support $HS(G)$, so that exactly one candidate is examined per graph. Applied to the House of Graphs database and to censuses of vertex-transitive graphs on at most 24 vertices, this pipeline recovers the Peres-Mermin square, the doily and the Mermin pentagram, and yields configurations reaching $\varepsilon = 0.707$, against $0.424$ for the previous published record. The best configurations are predominantly those stemming from line graphs and unions of graphs; we explain the former by showing that every perfect matching of a graph is a context of its line graph, which exhibits the Peres-Mermin square and the doily as the first members of two infinite families. We close with finite geometric descriptions of the most striking configurations inside symplectic polar spaces, in terms of ovoids, hyperbolic quadrics and Fano planes.
