Hierarchy of average correlation, quantum steering and Bell nonlocality in two-qubit systems

Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation Phys. Rev. Res. 5 023063 (2023), in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.