  In this work the Schmidt number of the two-photon state generated by
parametric-down conversion (PDC) is evaluated in the framework of a fully
spatio-temporal model for PDC. A comparison with the results obtained in either
purely spatial or purely temporal models shows that the degree of entanglement
of the PDC state cannot be trivially reduced to the product of the Schmidt
numbers obtained in models with lower dimensionality, unless the detected
bandwidth is very narrow. This result is a consequence of the non-factorability
of the state in the spatial and temporal degrees of freedoms of twin photons.
In the limit of a broad pump beam, we provide a geometrical interpretation of
the Schmidt number, as the ratio between the volume of the phase matching
region and of a correlation volume.
