Quantum theory of two-photon vector vortex beams

We develop the formal approach to a scheme for simultaneous generation of nonlocal quantum correlations in the spin and orbital degrees of freedom of hyperentangled photon pairs. 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.