## Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering

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Title Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering Jones, Steve James; Wiseman, Howard Mark; Doherty, A.C. Physical Review A (Atomic, Molecular and Optical Physics) Gordon W.F. Drake and Margaret Malloy 2007 Ridge, NY American Physical Society In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined steering'', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state, under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonstrates the nonlocal effect first identified in the famous EPR paper [Phys. Rev. {\bf 47}, 777 (1935)] as a universal effect for pure entangled states. This ability of Alice to remotely prepare Bob's state was subsequently called steering by Schr\"odinger, whose terminology we adopt. The phenomenon of steering has been largely overlooked, and prior to our work had not even been given a rigorous definition that is applicable to mixed states as well as pure states. Armed with our rigorous definition, we proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. In this work we expand on these results and provide further examples of steerable states. We also elaborate on the connection with the original EPR paradox. Yes Yes http://pra.aps.org/ http://dx.doi.org/10.1103/PhysRevA.76.052116 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. 76 052116-1 052116-18 1050-2947 2008-02-25 2009-10-13T21:49:49Z en_AU Centre for Quantum Dynamics Faculty of Science, Environment, Engineering and Technology PRE2009-Theoretical Physics http://hdl.handle.net/10072/18243 Journal Articles (Refereed Article) c1