General Monogamy Relation between Information-Theoretic Contextuality Inequalities

TL;DR

This paper establishes a tight condition for noncontextual descriptions in quantum systems using perfect commutation graphs and introduces a method to derive monogamy relations between contextuality inequalities, advancing understanding in quantum information theory.

Contribution

It introduces a novel method for proving monogamy relations between contextuality inequalities based on perfect commutation graphs, providing a new theoretical tool.

Findings

Perfect commutation graph is sufficient for noncontextual description.

Decomposition into perfect subgraphs enables monogamy relation proofs.

Theoretical results are experimentally verifiable.

Abstract

We show that the perfect commutation graph is the sufficient tight condition for admitting the noncontextual description of each observable set satisfying it in the yes-no question scenario. With this condition, we propose a method for proving the monogamy relation between two informationtheoretic contextuality inequalities by decomposing the total commutation graph into perfect subgraphs. The results offer a powerful tool to investigate the contextuality and to understand quantum information theory. This theoretical work can be experimentally verified in current laboratorial technology.