Recovering the full dimensionality of hyperentanglement in collinear photon pairs

Exploiting the simultaneous entanglement (hyperentanglement) in multiple degrees of freedom of an entangled photon pair increases the dimensionality of the Hilbert space for quantum information processing. However, the generation of hyperentangled photon pairs collinearly, while capable of high brightness, results in a smaller Hilbert space due to the two photons being in the same spatial mode. In this paper, we show that one can recover the full dimensionality of such hyperentanglement through a simple interference setup, similar to the time-reversed Hong-Ou-Mandel (TR-HOM) process. In contrast to the standard TR-HOM, we point out that a critical phase condition has to be satisfied in order to recover the hyperentanglement. We theoretically analyze the realization of this approach and discuss the feasibility of generating truly hyperentangled photon pairs. Our proposed approach does not require postselection and hence enables efficient hyperentangled photon pair generation for high-dimensional quantum applications.