Some remarks on Bell non-locality and Einstein-Podolsky-Rosen steering of bipartite states

TL;DR

This paper discusses the mathematical foundations and properties of Bell nonlocality and EPR steering in bipartite quantum states, including criteria for EPR steerability of maximally entangled states.

Contribution

It provides new mathematical characterizations and criteria for Bell nonlocality and EPR steering, including convexity, closedness, and steerability conditions.

Findings

Convexity and closedness of local and unsteerable state sets established.

Derived a new EPR-steering criterion for maximally entangled states.

Analyzed the mathematical structure of Bell nonlocality and EPR steering.

Abstract

Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked.