Chromatic Quantum Contextuality
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912314053099520 |
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| author | Svozil, Karl |
| author_facet | Svozil, Karl |
| contents | 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 n-uniform outcomes per context. Consequently, it cannot represent a "completable" non-contextual set of coexisting n-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 $n$-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chromatic Quantum Contextuality Svozil, Karl Quantum Physics 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 n-uniform outcomes per context. Consequently, it cannot represent a "completable" non-contextual set of coexisting n-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 $n$-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints. |
| title | Chromatic Quantum Contextuality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.15261 |