Noncontextual coloring of orthogonality hypergraphs
arXiv:2105.08520 · doi:10.1063/5.0062801
Abstract
We discuss representations and colorings of orthogonality hypergraphs in terms of their two-valued states interpretable as classical truth assignments. Such hypergraphs, if they allow for a faithful orthogonal representation, have quantum mechanical realizations in terms of intertwined contexts or maximal observables that are widely discussed as empirically testable criteria for contextuality. Reconstruction is possible for the class of perfectly separable hypergraphs. Colorings can be constructed from a minimal set of two-valued states. Some examples from exempt categories are presented that either cannot be reconstructed by two-valued states or whose two-valued states cannot yield a chromatic number that is equal to the maximal clique number.
arXiv comment35 pages, 11 figures, revised and final version
References in corpus (10)
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Finite precision measurement nullifies the Kochen-Specker theorem
- Kochen-Specker Vectors
- A variant of the Kochen-Specker theorem localising value indefiniteness
- Coloring the rational quantum sphere and the Kochen-Specker theorem
- Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
- Gadget structures in proofs of the Kochen-Specker theorem
- What makes quantum clicks special?
- Orthogonal Representation of Graphs
- Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis