  The amount of entanglement that exists in a parametric down-converted state
is investigated in terms of all the degrees of freedom of the state. We
quantify the amount of entanglement by the Schmidt number of the state,
represented as a pure bipartite state by tagging the down-converted photons in
terms of orthogonal states of polarization with the aid of type II
phase-matching. To facilitate our calculations, we use a Wigner functional
approach, which allows the incorporation of the full infinite dimensional
spatiotemporal degrees of freedom. A quantitative example with reasonably
achievable experimental conditions is considered to demonstrate that extremely
large Schmidt numbers are achievable.
