  We provide a detailed description of the EPR paradox (in the Bohm version)
for a two qubit-state in the discrete Wigner function formalism. We compare the
probability distributions for two qubit relevant to simultaneously-measurable
observables (computed from the Wigner function) with the probability
distributions representing two perfectly-correlated classic particles in a
discrete phase-space. We write in both cases the updating formulae after a
measure, thus obtaining a mathematical definition of \textit{classic collapse}
and \textit{quantum collapse}. We study, with the EPR experiment, the joint
probability distributions of Alice's and Bob's qubit before and after the
measure, analyzing the non-local effects. In particular, we give a more precise
definition of locality, which we call m-locality: we show that quantum systems
may violate this kind of locality, thus preserving, in an EPR-like argument,
the completeness of Quantum Mechanics.
