Chromatic Quantum Contextuality

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with <i>n</i>-uniform outcomes...

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Main Author: Karl Svozil
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Entropy
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Online Access:https://www.mdpi.com/1099-4300/27/4/387
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author Karl Svozil
author_facet Karl Svozil
author_sort Karl Svozil
collection DOAJ
description Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with <i>n</i>-uniform outcomes per context. Consequently, it cannot represent a “completable” noncontextual set of coexisting <i>n</i>-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to <i>n</i>-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints.
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spelling doaj-art-9be524f6da9e42ba9bfe41ea0f7577472025-08-20T03:13:51ZengMDPI AGEntropy1099-43002025-04-0127438710.3390/e27040387Chromatic Quantum ContextualityKarl Svozil0Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, AustriaChromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with <i>n</i>-uniform outcomes per context. Consequently, it cannot represent a “completable” noncontextual set of coexisting <i>n</i>-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to <i>n</i>-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints.https://www.mdpi.com/1099-4300/27/4/387contextualitylogichypergraphchromatic number
spellingShingle Karl Svozil
Chromatic Quantum Contextuality
Entropy
contextuality
logic
hypergraph
chromatic number
title Chromatic Quantum Contextuality
title_full Chromatic Quantum Contextuality
title_fullStr Chromatic Quantum Contextuality
title_full_unstemmed Chromatic Quantum Contextuality
title_short Chromatic Quantum Contextuality
title_sort chromatic quantum contextuality
topic contextuality
logic
hypergraph
chromatic number
url https://www.mdpi.com/1099-4300/27/4/387
work_keys_str_mv AT karlsvozil chromaticquantumcontextuality