Svozil Karl
Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria.
Entropy (Basel). 2025 Apr 5;27(4):387. doi: 10.3390/e27040387.
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 -uniform outcomes per context. Consequently, it cannot represent a "completable" noncontextual set of coexisting -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.
色量子情境性是一种基于（超）图着色约束的量子非经典性标准。如果一个量子超图所需的颜色数比每个最大可观测量（情境）的结果数多，那么它就缺乏每个情境具有均匀结果的经典实现。因此，它不能表示每个最大可观测量共存的(n)元结果的“可完备化”非情境集。这一结果是科亨 - 施佩克尔定理的色类似物。我们给出了一个三维中可四着色的量子逻辑的明确例子。此外，色情境性对经典真值提出了一种新的限制，从而排除了不能扩展为(n)元着色的二值测度。利用这个框架，我们为房子、五边形和五角星超图建立了新的界限，改进了先前的约束。
