  We explore, both experimentally and theoretically, the propagation dynamics
of spatially entangled photon pairs (biphotons). Characterization of
entanglement is done via the Schmidt number, which is a universal measurement
of the degree of entanglement directly related to the non-separability of the
state into its subsystems. We develop expressions for the terms of the Schmidt
number that depend on the amplitude and phase of the commonly used
double-Gaussian approximation for the biphoton wave function, and demonstrate
migration of entanglement between amplitude and phase upon propagation. We then
extend this analysis to incorporate both phase curvature in the pump beam and
higher spatial frequency content of more realistic non-Gaussian wave functions.
Specifically, we generalize the classical beam quality parameter M2 to the
biphotons, allowing the description of more information-rich beams and more
complex dynamics. Agreement is found with experimental measurements using
direct imaging and Fourier optics.
