Continuous frequency entanglement: Effective finite Hilbert space and entropy control

We examine the quantum structure of continuum entanglement and in the context of short-pulse down-conversion we answer the open question of how many of the uncountably many frequency modes contribute effectively to the entanglement. We derive a set of two-photon mode functions that provide an exact, discrete, and effectively finite basis for characterizing pairwise entanglement. Our analysis provides a basis for entropy control in two-photon pulses generated from down-conversion.