Optimal and tight Bell inequalities for state-independent contextuality sets

TL;DR

This paper identifies optimal Bell inequalities that maximize the robustness of nonlocality derived from state-independent contextuality sets, enabling practical experimental tests of quantum contextuality and nonlocality synergy.

Contribution

It introduces Bell inequalities with maximal robustness for SI-C sets, facilitating experimental verification of nonlocality and contextuality in quantum systems.

Findings

Bell inequalities with optimal noise resistance identified

Nonlocality from SI-C sets shown to be experimentally feasible

Enhanced robustness enables practical tests of quantum contextuality

Abstract

Two fundamental quantum resources, nonlocality and contextuality, can be connected through Bell inequalities that are violated by state-independent contextuality (SI-C) sets. These Bell inequalities allow for applications that require simultaneous nonlocality and contextuality. However, for existing Bell inequalities, the nonlocality produced by SI-C sets is very sensitive to noise. This precludes experimental implementation. Here we identify the Bell inequalities for which the nonlocality produced by SI-C sets is optimal, i.e., maximally robust to either noise or detection inefficiency, for the simplest SI-C [S. Yu and C. H. Oh, Phys. Rev. Lett. 108, 030402 (2012)] and Kochen-Specker sets [A. Cabello et al., Phys. Lett. A 212, 183 (1996)] and show that, in both cases, nonlocality is sufficiently resistant for experiments. Our work enables experiments that combine nonlocality and contextuality and therefore paves the way for applications that take advantage of their synergy.