Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes

TL;DR

This paper provides a complete geometric criterion for determining when a two-qubit quantum state is steerable under projective measurements, advancing the understanding of quantum correlations.

Contribution

It introduces a necessary and sufficient condition for two-qubit steerability based on the critical radius of local models, using a geometric approach.

Findings

Derived a criterion linking steerability to the critical radius of local models.

Calculated the critical radius for T-states and proved the optimality of a local hidden state model.

Established that a state is steerable if and only if its critical radius is less than 1.

Abstract

Fully characterizing the steerability of a quantum state of a bipartite system has remained an open problem since the concept of steerability was defined. In this work, using our recent geometrical approach to steerability, we suggest a necessary and sufficient condition for a two-qubit state to be steerable with respect to projective measurements. To this end, we define the critical radius of local models and show that a state of two qubits is steerable with respect to projective measurements from Alice's side if and only if her critical radius of local models is less than $1$. As an example, we calculate the critical radius of local models for the so-called T-states by proving the optimality of a recently-suggested ansatz for Alice's local hidden state model.