  We study the possibility of giving a classical interpretation to quantum
projective measurements for a particle described by a pure Gaussian state whose
Wigner function is non-negative. We analyze the case of a projective
measurement which gives rise to a proper Wigner function, i.e., taking on, as
its values, the eigenvalues of the projector. We find that, despite having this
property, this kind of projector produces a state whose Wigner function ceases
to be non-negative and hence precludes its interpretation as a classical
probability density. We also study the general case in which the projected
state has a non-negative Wigner function; but then we find that the Wigner
function of the projector is not a proper one. Thus, we conclude that a
non-negative Wigner function is inadequate to serve as a hidden variable model
for quantum processes in which projective measurements take place.
