Monogamy of Bell correlations and Tsirelson's bound

TL;DR

This paper explores the fundamental limits of quantum nonlocality in tripartite systems, generalizing Tsirelson's bound to characterize the trade-offs in Bell correlations among three parties.

Contribution

It introduces a new framework for understanding the monogamy of Bell correlations, extending Tsirelson's bound to arbitrary dimensions and measurement settings.

Findings

Derived a generalized trade-off relation for Bell correlations among three parties.

Revealed how Bell violations are constrained by local observable properties.

Connected Bell violations with local anticommuting observables.

Abstract

We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the Bell correlations observed by AB and of those observed by AC. This generalizes Tsirelson's bound on the quantum value of the CHSH inequality, the latter being recovered when C is completely uncorrelated with AB. We also discuss the trade-off between Bell violations and local expectation values of observables that anticommute with the ones used in the Bell test.