Four Party Absolutely Maximal Contextual Correlations
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Quantum Physics arXiv:2602.23883 (quant-ph) [Submitted on 27 Feb 2026] Title:Four Party Absolutely Maximal Contextual Correlations Authors:Nripendra Majumdar View a PDF of the paper titled Four Party Absolutely Maximal Contextual Correlations, by Nripendra Majumdar View PDF HTML (experimental) Abstract:The Kochen Specker theorem revealed contextuality as a fundamental nonclassical feature of nature. Nonlocality arises as a special case of contextuality, where entangled states shared by space like separated parties exhibit nonlocal correlations. The notion of maximality in correlations, analogous to maximal entanglement, is less explored in multipartite systems. In our work, we have defined maximal correlations in terms of contextual models, which are analogous to absolutely maximally entangled (AME) states. Employing the sheaf theoretic framework, we introduce maximal contextual correlations associated with the corresponding maximal contextual model. The formalism introduces the contextual fraction CF as a measure of contextuality, taking values from 0 (noncontextual) to 1 (fully contextual). This enables the formulation of a new class of correlations termed absolutely maximal contextual correlations (AMCC), which are both maximally contextual and maximal marginals. In the bipartite setting, the canonical example is the Popescu Rohrlich (PR) box, while in the tripartite case, it includes Greenberger Horne Zeilinger (GHZ) correlations and three way nonlocal correlations. In this work, we extend these findings to four party correlations. Notably, no AME state exists for four qubits, which introduces a subtle difference between AMCC and AME. The construction follows the constraint satisfaction problem (CSP) and parity check methods. In particular, the explicit realization of a non AMCC correlation that is maximally contextual yet not maximal marginal is obtained within the CSP framework. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.23883 [quant-ph] (or arXiv:2602.23883v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.23883 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nripendra Majumdar [view email] [v1] Fri, 27 Feb 2026 10:21:55 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Four Party Absolutely Maximal Contextual Correlations, by Nripendra MajumdarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)