Generation of hyperentangled states and two-dimensional quantum walks using J or q plates and polarization beam splitters

Abstract

A single photon can be made to entangle simultaneously in its different internal degrees of freedom (DoF)---polarization, orbital angular momentum (OAM), and frequency---as well as in its external DoF---path. Such entanglement in multiple DoF is known as hyperentanglement and provides additional advantage for quantum information processing. We propose a passive optical setup using $q$ plates and polarization beam splitters to hyperentangle an incoming single photon in polarization, OAM, and path DoF. By mapping polarization DoF to a two-dimensional coin state, and path and OAM DoF to two spatial dimensions, $x$ and $y$, we present a scheme for realization of a two-dimensional discrete-time quantum walk using only polarization beam splitters and $q$ plates ensuing the generation of hyperentangled states. The amount of hyperentanglement generated is quantified by measuring the entanglement negativity between any two DoF. We further show that hyperentanglement generation can be controlled by using an additional coin operation or by replacing the $q$ plate with a $J$ plate.