Universal scheme for violation of local realism from quantum advantage in one-way communication complexity

TL;DR

This paper establishes a universal connection between quantum communication complexity advantages and violations of local realism, introducing new Bell inequalities with exponential quantum-classical gaps.

Contribution

It provides the first explicit Bell inequality with binary observables and demonstrates an exponential violation linked to quantum advantage in communication complexity.

Findings

Universal equivalence between communication protocols and non-signaling correlations

Construction of new Bell inequalities with binary observables

Exponential quantum-classical violation gap

Abstract

We consider relations between communication complexity problems and detecting correlations (violating local realism) with no local hidden variable model. We show first universal equivalence between characteristics of protocols used in that type of problems and non-signaling correlations. We construct non linear bipartite Bell type inequalities and strong nonlocality test with binary observables by providing general method of Bell inequalities construction and showing that existence of gap between quantum and classical complexity leads to violation of these inequalities. We obtain, first to our knowledge, explicit Bell inequality with binary observables and exponential violation.