Degrees, Levels, and Profiles of Contextuality

Quantum Physics [Submitted on 16 Mar 2026] Degrees, Levels, and Profiles of Contextuality Ehtibar N. Dzhafarov, Victor H. Cervantes We introduce a new notion, that of a contextuality profile of a system. 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, \begin{array}{c|c|c|c|c|c|c|c} \textnormal{level} & 1 & \cdots & n-1 & n>1 & n+1 & \cdots & N\\ \hline \textnormal{degree} & 0 & \cdots & 0 & d_{n}>0 & d_{n+1}\geq d_{n} & \cdots & d_{N}\geq d_{N-1} \end{array} ,where N is the maximum number of variables per system's context. A system is represented at level n if one only considers the joint distributions with k\leq 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. Comments: 27 pp. 15 figures, 8 tables Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Probability (math.PR) MSC classes: 81P13, 81Q99, 60A99 Cite as: arXiv:2603.26692 [quant-ph]   (or arXiv:2603.26692v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26692 Focus to learn more Submission history From: Ehtibar Dzhafarov [view email] [v1] Mon, 16 Mar 2026 08:58:27 UTC (457 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.AI math math.PR References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)