Local-hidden-state models for Bell diagonal states and beyond

TL;DR

This paper develops optimal local-hidden-state models for Bell diagonal states and derives a criterion for unsteerability, advancing understanding of quantum steering and state characterization.

Contribution

It introduces a method to construct LHS models for Bell diagonal states by converting from Werner states, providing optimal models and a unsteerability criterion.

Findings

Optimal LHS models for Bell diagonal states derived

Conversion from Werner states simplifies model construction

Sufficient criterion for unsteerability established

Abstract

For a bipartite entangled state shared by two observers, Alice and Bob, Alice can affect the post-measured states left to Bob by choosing different measurements on her half. Alice can convince Bob that she has such an ability if and only if the unnormalized postmeasured states cannot be described by a local-hidden-state (LHS) model. In this case, the state is termed steerable from Alice to Bob. By converting the problem to construct LHS models for two-qubit Bell diagonal states to the one for Werner states, we obtain the optimal models given by Jevtic \textit{et al.} [J. Opt. Soc. Am. B 32, A40 (2015)], which are developed by using the steering ellipsoid formalism. Such conversion also enables us to derive a sufficient criterion for unsteerability of any two-qubit state.