Geometric Steering Criterion for Two-qubit States

TL;DR

This paper introduces a geometric steering criterion for two-qubit states that is both necessary and sufficient, providing a new way to quantify steerability and identify unsteerable entangled states.

Contribution

It presents a novel geometric criterion for two-qubit state steering, along with a quantification method for steerability and a procedure to generate unsteerable entangled states.

Findings

The criterion is necessary and sufficient for two-qubit states under arbitrary measurements.

A new measure quantifies the resources needed for measurement assemblages.

Constructed entangled states that are unsteerable under all projective measurements.

Abstract

According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A quantity is introduced to describe the required local resources to reconstruct a measurement assemblage for two-qubit states. We show that the quantity can be regarded as a quantification of steerability and be used to find out optimal LHS models. Finally we propose a method to generate unsteerable states, and construct some two-qubit states which are entangled but unsteerable under all projective measurements.