Chromatic Quantum Contextuality

• URL: http://arxiv.org/abs/2501.15261v3
• Date: Mon, 07 Apr 2025 20:41:12 GMT
• Title: Chromatic Quantum Contextuality
• Authors: Karl Svozil,
• Abstract summary: A quantum hypergraph requires more colors than the number of outcomes per maximal observable (context)<n>It cannot represent a "completable" non-contextual set of coexisting n-ary outcomes per maximal observable.<n>We present an explicit example of a four-colorable quantum logic in dimension three.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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