All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal

TL;DR

This paper introduces a new inequality that fully characterizes EPR-steering in two-qubit systems, showing that all states exhibiting CHSH-type correlations are also Bell nonlocal.

Contribution

The authors derive a necessary and sufficient inequality for EPR-steering based on CHSH-type correlations, generalizing previous results and establishing a direct link to Bell nonlocality.

Findings

Violation of the inequality confirms EPR-steering with minimal measurement settings

Maximum violation matches that of the CHSH inequality for the same state

All CHSH-type steerable states are also Bell nonlocal

Abstract

We derive a new inequality that is necessary and sufficient to show EPR-steering in a scenario employing only correlations between two arbitrary dichotomic measurements on each party. Thus the inequality is a complete steering analogy of the CHSH inequality, a generalisation of the result of Cavalcanti et al, JOSA B, 32(4), A74 (2015). We show that violation of the inequality only requires measuring over equivalence classes of mutually unbiased measurements on the trusted party and in fact assuming a general two qubit system arbitrary pairs of distinct projective measurements at the trusted party are equally useful. Via this it is found that for a given state the maximum violation of our EPR-steering inequality is equal to that for the CHSH inequality, so all states that are EPR-steerable with CHSH-type correlations are also Bell nonlocal.