Bell’s inequality violation with non-negative Wigner functions

M. Revzen, P. A. Mello, A. Mann, and L. M. Johansen
Phys. Rev. A 71, 022103 – Published 10 February 2005

Abstract

A Bell inequality violation allowed by the two-mode squeezed state, whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables that cannot be interpreted via a local hidden variable theory. Explicit calculations and interpretation are given for Bell’s suggestion that the EPR (Einstein, Podolsky, and Rosen) state will not allow violation of Bell’s inequality, in conjunction with its Wigner representative being nonnegative. It is argued that Bell’s theorem disallowing the violation of Bell’s inequality within a local hidden-variable theory depends on the dynamical variables having a definite value—assigned by the local hidden variables—even when they cannot be simultaneously measured. The analysis leads us to conclude that Bell’s inequality violation is to be associated with endowing these definite values to the dynamical variables, and not with their locality attributes.

  • Received 14 July 2004

DOI:https://doi.org/10.1103/PhysRevA.71.022103

©2005 American Physical Society

Authors & Affiliations

M. Revzen1, P. A. Mello2, A. Mann1, and L. M. Johansen3

  • 1Department of Physics, Technion—Israel Institute of Technology, Haifa 32000, Israel
  • 2Instituto de Física, Universidad Nacional Autónoma de México, 01000 México Distrito Federal, Mexico
  • 3Department of Technology, Buskerud University College, Kongsberg, Norway

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Issue

Vol. 71, Iss. 2 — February 2005

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