Degrees, Levels, and Profiles of Contextuality

Quantum Physics arXiv:2603.26692 (quant-ph) [Submitted on 16 Mar 2026] Title:Degrees, Levels, and Profiles of Contextuality Authors:Ehtibar N. Dzhafarov, Victor H. Cervantes View a PDF of the paper titled Degrees, Levels, and Profiles of Contextuality, by Ehtibar N. Dzhafarov and Victor H. Cervantes View PDF HTML (experimental) Abstract: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: 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 arXiv-issued DOI via DataCite Submission history From: Ehtibar Dzhafarov [view email] [v1] Mon, 16 Mar 2026 08:58:27 UTC (457 KB) Full-text links: Access Paper: View a PDF of the paper titled Degrees, Levels, and Profiles of Contextuality, by Ehtibar N. Dzhafarov and Victor H. CervantesView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.AI math math.PR References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)