Generation of hyperentangled states and two-dimensional quantum walks using $J$- ($q$)- plates and polarization beamsplitters

TL;DR

This paper proposes a passive optical setup using $q$-plates and polarization beamsplitters to generate hyperentangled states in multiple degrees of freedom of a single photon, enabling two-dimensional quantum walks for advanced quantum information processing.

Contribution

It introduces a novel passive optical scheme for hyperentangling photons in polarization, OAM, and path, and demonstrates how to realize 2D quantum walks with controllable hyperentanglement.

Findings

Successfully generates hyperentangled states in multiple DoF.

Quantifies entanglement using negativity measure.

Shows control of hyperentanglement via coin operations and $J$-plates.

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 provide additional advantage for quantum information processing. We propose a passive optical setup using $q$-plates and polarization beamsplitters 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 two-dimensional discrete-time quantum walk using only polarization beamsplitters 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 the hyperentanglement generation can be controlled by using an additional coin operation or by replacing the $q$-plate with a $J$-plate.