Relationship between average correlation and quantum steering for arbitrary two-qubit states

TL;DR

This paper explores the quantitative relationship between average correlation and quantum steering in two-qubit states, establishing bounds, characterizing states, and analyzing dynamics under noise, revealing a hierarchy of nonclassicality.

Contribution

It provides the first exact bounds linking average correlation and quantum steering, characterizes states achieving these bounds, and analyzes their behavior under noisy channels.

Findings

Bounds of average correlation versus steering are derived.

States achieving the bounds are characterized.

Dynamics under noisy channels are analyzed.

Abstract

Quantum nonlocality and nonclassicality are two remarkable characteristics of quantum theory, and offer quantum advantages in some quantum information processing. Motivated by recent work on the interplay between nonclassicality quantified by average correlation [Tschaffon et al., Phys. Rev. Res. 5,023063 (2023)] and Bell nonlocality, in this paper we aim to establish the relationship between the average correlation and the violation of the three-setting linear steering inequality for two-qubit systems. Exact lower and upper bounds of average correlation versus steering are obtained, and the respective states which suffice those bounds are also characterized. For clarity of our presentation, we illustrate these results with examples from well-known classes of two-qubit states. Moreover, the dynamical behavior of these two quantifiers is carefully analyzed under the influence of local unital and nonunital noisy channels. The results suggest that average correlation is closely related to the violation of three-setting linear steering, like its relationship with Bell violation. Particularly, for a given class of states, the hierarchy of nonclassicality-steering-Bell nonlocality is demonstrated.