Nonconvexity as the Analytic Shadow of Contextuality

Nonconvexity as the Analytic Shadow of Contextuality | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonconvexity as the Analytic Shadow of Contextuality Arash Zaghi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8168236/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We develop a convex-analytic framework that turns algebraic obstructions to global sections in sheaf models of quantum contextuality into certifiable signatures on quantum state space. For a finite family of projective measurement contexts we consider, for each context, the entropy increase incurred by dephasing in that context and the lower envelope of these associated classicalisation costs. Mathematically, we show that this envelope is convex exactly when a single classical frame can explain all statistics; genuine contextuality generically produces kinks and strictly positive Jensen gaps along chords, an epigraph-union manifestation of the failure of a global section. We obtain dimension- and overlap-dependent lower and upper bounds on these gaps using relative-entropy inequalities, and show that the resulting convexity defects are monotone under dephasing-covariant quantum channels. Operationally, the framework requires only context-wise frequency tables, yields finite-sample-robust witnesses and visual diagnostics, and is directly implementable on cloud quantum devices. A contextual Landauer principle links algebraic incompatibility of contexts to a nonzero minimal erasure work in branched-then-erase protocols. Taken together, these results provide algebraic and geometric invariants of measurement covers that translate foundational features of contextuality into experiment-ready benchmarks for contemporary quantum hardware. quantum contextuality nonconvexity information projection relative entropy (KL divergence) dephasing channel contextuality witnesses resource theory of contextuality sheaf/cohomology obstructions thermodynamics of information Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8168236","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":558724119,"identity":"3201bb7d-1ba7-4b80-99e4-4f9f3e3c0198","order_by":0,"name":"Arash 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dephasing channel, contextuality witnesses, resource theory of contextuality, sheaf/cohomology obstructions, thermodynamics of information","lastPublishedDoi":"10.21203/rs.3.rs-8168236/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8168236/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe develop a convex-analytic framework that turns algebraic obstructions to global sections in sheaf models of quantum contextuality into certifiable signatures on quantum state space. 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