Quantum correlations for arbitrarily high-dimensional Bell inequality

TL;DR

This paper investigates the structure of bipartite high-dimensional Bell inequalities using correlators, revealing their necessity and maximal violations by Bell states, thus advancing understanding of quantum correlations.

Contribution

It introduces novel correlation conditions based on correlators for bipartite high-dimensional Bell inequalities, showing their necessity and relation to maximal quantum violations.

Findings

Correlators are essential elements of Bell inequalities.

Maximal violations by Bell states satisfy the correlation conditions.

Bell inequalities can be expressed in terms of correlators.

Abstract

We analyze the correlation structure of bipartite arbitrary-dimensional Bell inequalities via novel conditions of correlations in terms of differences of joint probabilities called correlators. The conditions of correlations are shown to be necessary for the multi-level Bell state. In particular, we find that the bipartite arbitrary-dimensional Bell-type inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)] are composed of correlators, and we reveal that the maximal violations by the Bell state just fit the conditions of quantum correlations. Correlators can be considered as essential elements of Bell inequalities.