Twin inequality for fully contextual quantum correlations

TL;DR

This paper introduces a new tight inequality, twin to the KCBS inequality, which precisely characterizes the limits of quantum contextuality, serving as a fundamental tool for understanding quantum correlations.

Contribution

It presents a novel tight inequality twin to the KCBS inequality that fully captures quantum contextual correlations, advancing the understanding of quantum contextuality.

Findings

Quantum mechanics exhibits unique contextuality.

The twin inequality cannot be outperformed by more general theories.

It provides a simple criterion for recognizing fully contextual quantum correlations.

Abstract

Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextual quantum correlations.