Steering, Entanglement, nonlocality, and the Einstein-Podolsky-Rosen Paradox
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The concept of steering was introduced by Schrodinger in 1935 as a generalization of the EPR 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 EPR paradox.
Physical Review Letters
Copyright 2007 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.