We introduce a new notion, that of a contextuality profile of a system of random variables. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered. A system is represented at level n if one only considers the joint distributions with no more than n variables, ignoring higher-order joint distributions. We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality. We present a method of concatenated systems to explore contextuality profiles systematically, and we apply it to the contextuality profiles for three major measures of contextuality proposed in the literature.

翻译：我们引入一个新概念——随机变量系统的背景性剖面。不同于用单一数值（即系统的整体背景性程度）来表征其背景性，我们展示了如何通过一条曲线来描述系统的背景性，该曲线将背景性程度与系统被考虑的层次相关联。如果一个系统仅考虑不超过n个变量的联合分布，而忽略更高阶的联合分布，则该系统被视为在层次n上表示。我们证明，层次化的背景性分析可以与任何构造良好的背景性度量结合使用。我们提出了一种通过串联系统系统性地探索背景性剖面的方法，并将其应用于文献中提出的三种主要背景性度量的背景性剖面分析。