Polarization-momentum hyper-entangled two photon states

We present a parametric source which allows the engineering of polarization-momentum hyper-entangled two photon states based on linear optics and a single type-I nonlinear crystal. The nonlocal character of these states has been verified by various tests, including, the "All Versus Nothing" test of local realism [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001)], which represents a generalization of the GHZ to the case of two entangled particles and two observers. We have also created a complete and deterministic Bell-state measurement by a novel experimental scheme which adopts polarization-momentum hyper-entanglement and requires linear optics and single photon detectors