Simple conditions constraining the set of quantum correlations

TL;DR

This paper introduces simple analytical conditions that are necessary for bipartite behaviors to be quantum, aiding the understanding and characterization of quantum correlations in Bell scenarios.

Contribution

It provides the first general necessary conditions for quantum correlations, with applications to Tsirelson bounds and Bell inequalities.

Findings

Necessary conditions distinguish quantum from non-quantum behaviors

Quantitative separation of quantum and nonlocal no-signaling sets

Construction of Bell expressions maximized by maximally entangled states

Abstract

The characterization of the set of quantum correlations in Bell scenarios is a problem of paramount importance for both the foundations of quantum mechanics and quantum information processing in the device-independent scenario. However, a clear-cut (physical or mathematical) characterization of this set remains elusive and many of its properties are still unknown. We provide here simple and general analytical conditions that are necessary for an arbitrary bipartite behaviour to be quantum. Although the conditions are not sufficient, we illustrate the strength and non-triviality of these conditions with a few examples. Moreover, we provide several applications of this result: we prove a quantitative separation of the quantum set from extremal nonlocal no-signaling behaviours in several general scenarios, we provide a relation to obtain Tsirelson bounds for arbitrary Bell inequalities and a construction of Bell expressions whose maximal quantum value is attained by a maximally entangled state of any given dimension.