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arXiv:2109.11158 · Physical Review A

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

P. A. Ameen Yasir, C. M. Chandrashekar

Published Jan 18, 2022• 16 citations
arXivHTMLPDF

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.

DOI
10.1103/physreva.105.012417

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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 qqq 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, xxx and yyy, we present a scheme for realization of a two-dimensional discrete-time quantum walk using only polarization beam splitters and qqq 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 qqq plate with a JJJ plate.
Abstract Higher dimensional Hilbert space along with ability to control multiple degrees of freedom of photon and entangle them has enabled new quantum protocols for various quantum information processing applications. Here, we propose a scheme to generate and control polarization-path-frequency entanglement using the operative elements required to implement a polarization-controlled quantum walk in the path (position) space and frequency domain. Hyperentangled states manifests in the controlled dynamics using an interferometric setup where half-wave plates, beam-splitters and frequency shifters such as those based on the electro-optic effect are used to manipulate the polarization, path and frequency degrees of freedom respectively. The emphasis is on utilizing the polarization to influence the movement to a specific value in the frequency and position space. Negativity between the subspaces is calculated to demonstrate the controllability of the entanglement between the three degrees of freedom and the effect of noise on the entanglement is modelled using the depolarizing channel. Progress reported with experimental demonstration of realization of quantum walk using quantum states of light makes quantum walks a practical approach to generate hyperentangled states.
Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for the verification of high-dimensional entanglement in the combined state space. These results may indicate new paths towards practical exploitation of entanglement stored in multiple degrees of freedom, in particular in the context of high-dimensional quantum information processing protocols.
We experimentally demonstrate a scheme for the preparation of high-dimensional hyperentangled photon pairs with path degree of freedom (DOF) and orbital-angular-momentum (OAM) DOF using beam displacer (BD) interferometers from a warm atomic ensemble. A strong Gaussian pump beam of fixed frequency passes through the BD to produce a superposition state of two paths. The biphoton state is generated from two parallel spontaneous four-wave mixing processes in the 85Rb^{85}\mathrm{Rb}85Rb vapor cell. We successfully detect the path entanglement, two-dimensional OAM entanglement, and three-dimensional OAM entanglement by selecting the appropriate measurement. Due to the advantages of the simplicity of our interaction system and high dimensionality of the narrowband hyperentangled photons we generated, such hyperentangled source from an atomic ensemble can be utilized to realize high-dimensional multiple-DOF quantum memory and quantum communication in the future.
Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.
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We investigate quantum entanglement of three photons performing discrete-time quantum walk (DTQW) on the nearest-neighbor sites of a square lattice. Such a DTQW setup has already been proposed to be realizable using linear optical elements. Each lattice site corresponds to the sequential action of a half-wave plate and a polarizing beam splitter. Two-dimensional DTQW can be mapped to an effective one-dimensional DTQW with a four-sided coin that depends on the polarization and direction of motion of the photons. It is known that such a system is capable to spatially entangle two photons, prepared in a separable state initially. We generalize the result to the case of three photons to explore if distinct entanglement classes, namely W and GHZ states, can be produced by this setup. In addition to spatial entanglement, we analyze the possibility of entanglement in the polarization basis, too. Our results can be significant for a simple and fast generation of multipartite entangled photonic states demanded by practical quantum technology applications.