  We develop the formal approach to the angular spectrum transfer in parametric
down-conversion that allows pumping with a structured beam. The scheme is based
on an entangled photon source pumped by a laser beam structured with a
vector-vortex polarization profile. This creates a two-photon quantum state
exhibiting polarization-dependent transverse correlations that can be accessed
through coincidence measurements on the spatially separated photons. The
calculated correlations are shown to present a spin-orbit profile typical of
vector beams, however, distributed on separate measurement regions. Our
approach allows the design of the pump beam vector spatial structure and
measurement strategies for potential applications of these entangled states,
such as in quantum communication.
