Bell’s inequality violation with non-negative Wigner functions

Abstract

A Bell inequality violation (BIQV) allowed by the two-mode squeezed state (TMSS), whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables (DV) that cannot be interpreted via a local hidden variable (LHV) theory. Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky and Rosen) state will not allow for BIQV in conjuction with its Wigner representative state 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 DV's having a definite value --assigned by the LHV-- even when they cannot be simultaneously measured. The analysis leads us to conclude that BIQV is to be associated with endowing these definite values to the DV's and {\it not} with their locality attributes.