Bell's inequality violation with non-negative Wigner functions

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.