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

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.

arXiv comment3 figures

References in corpus (18)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• The Uncertainty Relation for Smooth Entropies
• Experimental EPR-Steering of Bell-local States
• Quantification of Gaussian quantum steering
• Quantifying Einstein-Podolsky-Rosen steering
• Quantum Steering Ellipsoids
• Quantification of Einstein-Podolski-Rosen steering for two-qubit states
• Negativity and steering: a stronger Peres conjecture
• Asymmetric Gaussian steering: when Alice and Bob disagree
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Fine-grained EPR-steering inequalities
• The geometry of the Einstein--Podolsky--Rosen correlations
• Complementarity Relations Between Quantum Steering Criteria
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Entanglement as upper bounded for the nonlocality of a general two-qubit system
• Geometric Steering Criterion for Two-qubit States