A generalization of the CHSH inequality self-testing maximally entangled states of any local dimension

TL;DR

This paper introduces a family of generalized CHSH inequalities that can self-test maximally entangled states of any local dimension, advancing the understanding of quantum correlations and state certification.

Contribution

It presents the first family of inequalities that self-test maximally entangled states of arbitrary local dimension, extending the scope of self-testing methods.

Findings

Generalized CHSH inequalities for all dimensions $d \\geq 2$

Maximal violation self-tests maximally entangled states

Conjecture on inequalities for all pure bipartite entangled states

Abstract

For every $d \geq 2$, we present a generalization of the CHSH inequality with the property that maximal violation self-tests the maximally entangled state of local dimension $d$. This is the first example of a family of inequalities with this property. Moreover, we provide a conjecture for a family of inequalities generalizing the tilted CHSH inequalities, and we conjecture that for each pure bipartite entangled state there is an inequality in the family whose maximal violation self-tests it. All of these inequalities are inspired by the self-testing correlations of [Nat. Comm. 8, 15485 (2017)].