  We apply the Wigner function formalism to the study of two-photon
polarization-momentum hyperentanglement generated in parametric down
conversion. It is shown that the consideration of a higher number of degrees of
freedom is directly related to the extraction of additional uncorrelated sets
of zeropoint modes at the source. We present a general expression for the
description of the quantum correlations corresponding to the sixteen Bell base
states, in terms of four beams whose amplitudes are correlated through the
stochastic properties of the zeropoint field. A detailed analysis of the two
experiments on complete Bell-state measurement included in [Walborn et al.,
Phys. Rev. A 68, 042313 (2003)] is made, emphasizing the role of the zeropoint
field. Finally, we investigate the relationship between the zeropoint inputs at
the source and the analysers, and the limits on optimal Bell-state measurement.
