Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
1 Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany
2 Department of Mathematics, University of Nebraska-Lincoln - Lincoln, NE 68588, USA
Received: 17 May 2016
Accepted: 8 July 2016
Fully characterizing the steerability of a quantum state of a bipartite system has remained an open problem ever since the concept of steerability was first defined. In this paper, 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 local hidden state model.
PACS: 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.67.Mn – Entanglement measures, witnesses, and other characterizations
© EPLA, 2016