Quantification of Einstein-Podolski-Rosen steering for two-qubit states

TL;DR

This paper introduces a new measure for quantifying Einstein-Podolski-Rosen steering in two-qubit states based on the maximal violation of steering inequalities, providing simple formulas for different measurement scenarios.

Contribution

It proposes a novel steering measure derived from inequality violations, with closed-form formulas for two- and three-measurement cases, aligning with the entanglement-steering-nonlocality hierarchy.

Findings

The measure correctly reflects the hierarchy of quantum correlations.

Closed formulas simplify the evaluation of steerability.

The approach aligns with previously reported results.

Abstract

In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. Among the options investigated, a measure has been found that correctly satisfies the entanglement-steering-nonlocality hierarchy and reproduces results reported so far.