This article delves into the concept of quantum contextuality, specifically focusing on proofs of the Kochen-Specker theorem obtained by assigning Pauli observables to hypergraph vertices satisfying a given commutation relation. The abstract structure composed of this hypergraph and the graph of anticommutations is named a hypergram. Its labelings with Pauli observables generalize the well-known magic sets. A first result is that all these quantum labelings satisfying the conditions of a given hypergram inherently possess the same degree of contextuality. Then we provide a necessary and sufficient algebraic condition for the existence of such quantum labelings and an efficient algorithm to find one of them. We finally attach to each assignable hypergram an abstract notion of contextuality degree. By presenting the study of observable-based Kochen-Specker proofs from the perspective of graphs and matrices, this abstraction opens the way to new methods to search for original contextual configurations.

翻译：本文深入探讨量子语境性概念，特别关注通过将泡利可观测量分配给满足给定对易关系的超图顶点所获得的Kochen-Specker定理证明。由该超图及其反对易关系图构成的抽象结构被称为超图字。其泡利可观测量标记推广了著名的魔术集合。首个结论是：满足给定超图字条件的所有量子标记本质上具有相同的语境性程度。随后我们给出了此类量子标记存在的充要代数条件，并提供一种高效算法以寻找其中一种标记。最后我们为每个可分配超图字赋予语境性程度的抽象概念。通过从图与矩阵的视角呈现基于可观测量Kochen-Specker证明的研究，这种抽象化为寻找新颖语境构型的新方法开辟了道路。