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The amount of entanglement that exists in a parametric down-converted stateis investigated in terms of all the degrees of freedom of the state. Wequantify the amount of entanglement by the Schmidt number of the state,represented as a pure bipartite state by tagging the down-converted photons interms of orthogonal states of polarization with the aid of type IIphase-matching. To facilitate our calculations, we use a Wigner functionalapproach, which allows the incorporation of the full infinite dimensionalspatiotemporal degrees of freedom. A quantitative example with reasonablyachievable experimental conditions is considered to demonstrate that extremelylarge Schmidt numbers are achievable.

Quantifying entanglement of parametric down-converted states in all degrees of freedom