Necessary and sufficient criterion of steering for two-qubit T states

TL;DR

This paper derives a necessary and sufficient steering criterion for two-qubit T states, linking steerability to entanglement measures and providing a practical method to estimate steerability via concurrence.

Contribution

The authors introduce a new infinite-measurement steering inequality that fully characterizes steerability of two-qubit T states, extending previous criteria.

Findings

Steerability is fully characterized by the new inequality.

All separable T states do not violate the inequality.

T state steerability correlates with concurrence exceeding 1/4.

Abstract

Einstein-Podolsky-Rosen (EPR) steering is the ability that an observer persuades a distant observer to share entanglement by making local measurements. Determining a quantum state is steerable or unsteerable remains an open problem. Here, we derive a new steering inequality with infinite measurements corresponding to an arbitrary two-qubit T state, from consideration of EPR steering inequalities with N projective measurement settings for each side. In fact, the steering inequality is also a sufficient criterion for guaranteering that the T state is unsteerable. Hence, the steering inequality can be viewed as a necessary and sufficient criterion to distinguish whether the T state is steerable or unsteerable. In order to reveal the fact that the set composed of steerable states is the strict subset of the set made up of entangled states, we prove theoretically that all separable T states can not violate the steering inequality. Moreover, we put forward a method to estimate the maximum violation from concurrence for arbitrary two-qubit T states, which indicates that the T state is steerable if its concurrence exceeds 1/4.