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      Negativity and contextuality are equivalent notions of nonclassicality

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          Abstract

          Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.

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          Author and article information

          Journal
          29 October 2007
          2008-06-30
          Article
          10.1103/PhysRevLett.101.020401
          0710.5549
          4acf012f-d71d-4962-81d4-727f1f1d3c4a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          Phys. Rev. Lett. 101, 020401 (2008)
          5 pages, published version (modulo some supplementary material)
          quant-ph

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