Quantum steerability based on joint measurability

TL;DR

This paper introduces an analytical method to quantify EPR-steerability in two-qubit states, linking joint measurability to steerability, and derives conditions and formulas for specific classes of states.

Contribution

It provides the first analytical formula for steerability of certain two-qubit states and characterizes conditions for two-setting EPR-steering.

Findings

Derived an analytical formula for steerability of X-states.

Established necessary and sufficient conditions for two-setting EPR-steering.

Identified a class of one-way steerable states.

Abstract

Occupying a position between entanglement and Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering has attracted increasing attention in recent years. Many criteria have been proposed and experimentally implemented to characterize EPR-steering. Nevertheless, only a few results are available to quantify steerability using analytical results. In this work, we propose a method for quantifying the steerability in two-qubit quantum states in the two-setting EPR-steering scenario, using the connection between joint measurability and steerability. We derive an analytical formula for the steerability of a class of X-states. The sufficient and necessary conditions for two-setting EPRsteering are presented. Based on these results, a class of asymmetric states, namely, one-way steerable states, are obtained.