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

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.

A new appendix has been included, where Jones matrices are realized using $J$-plates and variable waveplates

References in corpus (14)

• Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media
• Beating the channel capacity limit for linear photonic superdense coding
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Discrete single-photon quantum walks with tunable decoherence
• One-step deterministic polarization entanglement purification using spatial entanglement
• Long-distance entanglement purification for quantum communication
• Photonic quantum walk in a single beam with twisted light
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• Optimizing the discrete time quantum walk using a SU(2) coin
• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
• Symmetries and noise in quantum walk
• Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons
• Decoherence on a two-dimensional quantum walk using four- and two-state particle

Cited by in corpus (7)

• Designing three-way entangled and nonlocal two-way entangled single particle states via alternate quantum walks
• Noise resilience in path-polarization hyperentangled probe states
• Optical realization of one-dimensional generalized split-step quantum walks
• Quantum cryptographic protocols with dual messaging system via 2D alternate quantum walk of a genuine single-photon entangled state
• Deterministic generation of hybrid entangled states using quantum walks
• Polarization-path-frequency entanglement using interferometry and frequency shifters
• Phase vs coin vs position disorder as a probe for the resilience and revival of single particle entanglement in cyclic quantum walks