Chromatic Quantum Contextuality

TL;DR

This paper introduces chromatic quantum contextuality, a graph-coloring-based criterion for quantum nonclassicality, providing new bounds and examples that extend foundational theorems like Kochen-Specker.

Contribution

It develops a chromatic analogue of the Kochen-Specker theorem, presents explicit examples in dimension three, and refines bounds for specific hypergraphs using this framework.

Findings

Explicit example of a four-colorable quantum logic in dimension three

Refined bounds for house, pentagon, and pentagram hypergraphs

Chromatic contextuality excludes certain classical truth value assignments

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.