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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MDPI AG
2025-04-01
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| 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. |
| format | Article |
| id | doaj-art-9be524f6da9e42ba9bfe41ea0f757747 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| 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 |