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  • Letter
  • Open Access

Optimal and tight Bell inequalities for state-independent contextuality sets

Junior R. Gonzales-Ureta1,*, Ana Predojević1,†, and Adán Cabello2,3,‡

  • 1Department of Physics, Stockholm University, 10691 Stockholm, Sweden
  • 2Departamento de Física Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain
  • 3Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, 41012 Sevilla, Spain

  • *junior.gonzales@fysik.su.se
  • †ana.predojevic@fysik.su.se
  • ‡adan@us.es
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Phys. Rev. Research 5, L012035 – Published 10 March, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012035

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.

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Phys. Rev. Research 5, L012035– Published 10 March, 2023
  • Received 10 August 2022
  • Accepted 17 February 2023
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