Optimal inequalities for state-independent contextuality

TL;DR

This paper formulates the problem of finding optimal inequalities for state-independent quantum contextuality as a linear program, introducing the noncontextuality polytope and identifying tight inequalities for fundamental scenarios.

Contribution

It provides an exact linear programming approach to derive optimal inequalities for state-independent contextuality, generalizing the locality polytope concept.

Findings

Identified two tight optimal inequalities for fundamental quantum scenarios.

Introduced the noncontextuality polytope as a generalization of the locality polytope.

Demonstrated the linear program formulation for optimal inequality discovery.

Abstract

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correlations in an state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope, and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.