Nonlocal games, synchronous correlations, and Bell inequalities

TL;DR

This paper explores synchronous correlations in nonlocal games, establishing Bell-like inequalities, and introduces a symmetric, device-independent quantum key distribution protocol with proven security features and bounds.

Contribution

It derives Bell inequalities for synchronous correlations, introduces a novel symmetric quantum key distribution protocol, and proves bounds and rigidity results for quantum correlations in this setting.

Findings

No quantum Bell violation for two measurement settings in synchronous correlations.

Explicit Bell-like inequalities for three measurement settings are provided.

Existence and rigidity of quantum correlations saturating Tsirl'son's bound are demonstrated.

Abstract

Nonlocal games with synchronous correlations are a natural generalization of functions between two finite sets. In this work we examine analogues of Bell's inequalities for such correlations, and derive a synchronous device-independent quantum key distribution protocol. This protocol has the advantage of symmetry between the two users and self-testing while generating shared secret key without requiring a preshared secret. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlations with three measurement settings and two outputs, provide an analogue of Tsirl'son's bound in this setting, and prove existence and rigidity of quantum correlations that saturate this bound. We conclude by posing a security assumption that bypasses the locality, or causality, loophole and examine the protocol's robustness against measurement error and depolarization noise.