An entropic approach to local realism and noncontextuality

TL;DR

This paper develops a unified entropic framework for analyzing local realism and noncontextuality, deriving tight inequalities that are adaptable to complex scenarios like bilocality and detection inefficiencies.

Contribution

It introduces a novel entropic approach that simplifies the derivation of inequalities in nonlocal and contextuality scenarios, including those with additional independence constraints.

Findings

Derived tight entropic inequalities for various Bell and Kochen-Specker scenarios.

Showed that entropic inequalities adapt easily to bilocality and other complex scenarios.

Demonstrated that detection inefficiencies can be effectively incorporated, allowing for low-efficiency quantum contextuality tests.

Abstract

For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality) inequalities. In this paper we explore this entropic approach and derive tight entropic inequalities for various scenarios. One advantage of entropic inequalities is that they easily adapt to situations like bilocality scenarios, which have additional independence requirements that are non-linear on the level of probabilities, but linear on the level of entropies. Another advantage is that, despite the nonlinearity, taking detection inefficiencies into account turns out to be very simple. When joint measurements are conducted by a single detector only, the detector efficiency for witnessing quantum contextuality can be arbitrarily low.