A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality

TL;DR

This paper proves that any proof of the Kochen-Specker theorem, regardless of the method used, can be transformed into a state-independent noncontextuality inequality, providing a universal approach to reveal quantum contextuality.

Contribution

It establishes that all proofs of the Kochen-Specker theorem can be converted into noncontextuality inequalities, extending previous results and offering a general derivation method.

Findings

All types of Kochen-Specker proofs can be converted to noncontextuality inequalities.

Provides a constructive, general approach for deriving inequalities from proofs.

Confirms the universality of converting Kochen-Specker proofs to noncontextuality inequalities.

Abstract

Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether it is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the Kochen-Specker theorem.