Steering, Entanglement, Nonlocality, and the EinsteinPodolskyRosen Paradox
Abstract
The concept of steering was introduced by Schrödinger in 1935 as a generalization of the EinsteinPodolskyRosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original EinsteinPodolskyRosen paradox.
 Publication:

Physical Review Letters
 Pub Date:
 April 2007
 DOI:
 10.1103/PhysRevLett.98.140402
 arXiv:
 arXiv:quantph/0612147
 Bibcode:
 2007PhRvL..98n0402W
 Keywords:

 03.65.Ud;
 03.65.Ta;
 03.67.Mn;
 Entanglement and quantum nonlocality;
 Foundations of quantum mechanics;
 measurement theory;
 Entanglement production characterization and manipulation;
 Quantum Physics
 EPrint:
 4 pages, 1 figure. v3 updated version published in Phys. Rev. Lett