Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem

Understand

Kochen-Specker (KS) theorem reveals the inconsistency between quantum theory and any putative underlying model of it satisfying the constraint of KS-noncontextuality.

• A logical proof of the KS theorem is one that relies only on the compatibility relations amongst a set of projectors (a KS set) to witness this inconsistency.
• These compatibility relations can be represented by a hypergraph, referred to as a contextuality scenario.
• Here we consider contextuality scenarios that we term KS-uncolourable, e.g., those which appear in logical proofs of the KS theorem.