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We study the properties of the discrete Wigner distribution for two qubitsintroduced by Wotters. In particular, we analyze the entanglement propertieswithin the Wigner distribution picture by considering the negativity of theWigner function (WF) and the correlations of the marginal distribution. We showthat a state is entangled if at least one among the values assumed by thecorresponding discrete WF is smaller than a certain critical (negative) value.Then, based on the Partial Transposition criterion, we establish the relationbetween the separability of a density matrix and the non-negativity of the WF'srelevant both to such a density matrix and to the partially transposed thereof.  Finally, we derive a simple inequality --involving the covariance-matrixelements of a given WF-- which appears to provide a separability criterionstronger than the one based on the Local Uncertainty Relations.Comment: 15 pages, 6 table

Discrete Wigner distribution for two qubits: a characterization of entanglement properties