Chromatic Quantum Contextuality
arXiv:2501.15261 · doi:10.3390/e27040387
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 -ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints.
arXiv comment7 pages, 3 figures, final version
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