We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides a direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function describes correlations in the joint measurement of the phase space displaced parity operator.
@article{arxiv.quant-ph/9806069,
title = {Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation},
author = {Konrad Banaszek and Krzysztof Wodkiewicz},
journal= {arXiv preprint arXiv:quant-ph/9806069},
year = {2009}
}