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Contextuality as an Information-Theoretic Obstruction to Classical Probability

arXiv Quantum Physics
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⚡ Quantum Brief
Song-Ju Kim’s January 2026 study reframes quantum contextuality as an information-theoretic limitation, not just a nonclassical quirk. The work argues contextuality forces classical models to either encode context in their internal states or use external labels with nonzero information. The paper introduces a constraint: operational models must maintain a single internal state with fixed semantics across contexts. Under this rule, reproducing quantum statistics becomes impossible for classical systems without added informational overhead. Contextuality is recast as evidence of irreducible information cost in classical representations. Unlike prior views treating it as an anomaly, this work ties it to fundamental resource demands in classical simulations of quantum behavior. Quantum probability emerges as the only framework accommodating contextual operations without explicit contextual encoding. This positions quantum theory as uniquely efficient for handling context-dependent processes. The findings bridge abstract quantum foundations with practical information theory, offering a new lens to compare classical and quantum computational frameworks. The work suggests contextuality may define a hard boundary for classical emulation.
Contextuality as an Information-Theoretic Obstruction to Classical Probability

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Quantum Physics arXiv:2601.20167 (quant-ph) [Submitted on 28 Jan 2026] Title:Contextuality as an Information-Theoretic Obstruction to Classical Probability Authors:Song-Ju Kim View a PDF of the paper titled Contextuality as an Information-Theoretic Obstruction to Classical Probability, by Song-Ju Kim View PDF HTML (experimental) Abstract:Contextuality is a central feature distinguishing quantum from classical probability theories, yet its operational meaning remains subject to interpretation. We reconsider contextuality from an information-theoretic perspective, focusing on operational models constrained to maintain a single internal state with fixed semantics across multiple contexts. Under this constraint, we show that contextual statistics certify an unavoidable obstruction to classical probabilistic descriptions. Specifically, any classical model that reproduces such statistics must either embed contextual dependence into the internal state or introduce additional external labels carrying nonzero information. This result identifies contextuality as a witness of irreducible information cost in classical representations, rather than as a purely nonclassical anomaly. From this viewpoint, quantum probability emerges as a canonical framework that accommodates contextual operations without requiring explicit contextual encoding. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.20167 [quant-ph] (or arXiv:2601.20167v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20167 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Song-Ju Kim Dr. [view email] [v1] Wed, 28 Jan 2026 02:02:55 UTC (5 KB) Full-text links: Access Paper: View a PDF of the paper titled Contextuality as an Information-Theoretic Obstruction to Classical Probability, by Song-Ju KimView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)

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Source: arXiv Quantum Physics