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arXiv:2110.07183 · Frontiers in Physics

High-Dimensional Entanglement of Photonic Angular Qudits

Graciana Puentes

Published Apr 26, 2022• 1 citation
arXivHTMLPDF

Abstract

We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.

DOI
10.3389/fphy.2022.868522

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We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
Using angular position–orbital angular momentum entangled photons, we propose an experiment to generate maximally entangled states in D-dimensional quantum systems, the so called qudits, by exploiting correlations of parametric down-converted photons. Angular diffraction masks containing N angular slits in the arms of each twin photon define a qudit space of dimension N2, spanned by the alternative pathways of the photons. Numerical results for N angular slits with N = 2, 4, 5, 10 are reported. We discuss relevant experimental parameters for an experimental implementation of the proposed scheme using Spatial Light Modulators (SLMs), and twin-photons produced by Spontaneous Parametric Down Conversion (SPDC). The entanglement of the qudit state can be quantified in terms of the Concurrence, which can be expressed in terms of the visibility of the interference fringes, or by using Entanglement Witnesses. These results provide an additional means for preparing entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
An important problem in the practical application of high-dimensional two-photon orbital angular momentum (OAM) entanglement generated by spontaneous down conversion is a lower degree of entanglement, where the amplitudes of modes are not uniformly distributed. In contrast to the previously raised entanglement concentration protocol, we here report on an experimental scheme that addresses this problem by tuning the two-photon quantum angular position correlation. An opaque mask with N evenly distributed angular slits having a radius r is inserted in the two-photon down-conversion light path. The number N should be such that the separation of adjacent angular slits is larger than the scale of the two-photon angular position correlation. The OAM entanglement for the two-photon state after the opaque mask is cast into a set of folded subbands with a dimension of N, owing to the reduction of rotational symmetry from continuous invariance to discrete invariance. Almost maximum OAM entanglement can be realized by properly setting the width of the angular slits.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
Any practical experiment utilizing the innate DDD-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from 3.183.183.18 to 4.954.954.95 bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values 0.960.960.96 and 0.900.900.90. The good entanglement measures in both OAM and angular position bases indicate bipartite, DDD-dimensional entanglement where DDD is tunable.
Engineering single-photon states endowed with orbital angular momentum (OAM) is a powerful tool for quantum information photonic implementations. Indeed, due to its unbounded nature, OAM is suitable for encoding qudits, allowing a single carrier to transport a large amount of information. Most of the experimental platforms employ spontaneous parametric down-conversion processes to generate single photons, even if this approach is intrinsically probabilistic, leading to scalability issues for an increasing number of qudits. Semiconductor quantum dots (QDs) have been used to get over these limitations by producing on-demand pure and indistinguishable single-photon states, although only recently they have been exploited to create OAM modes. Our work employs a bright QD single-photon source to generate a complete set of quantum states for information processing with OAM-endowed photons. We first study hybrid intraparticle entanglement between OAM and polarization degrees of freedom of a single photon whose preparation was certified by means of Hong–Ou–Mandel visibility. Then, we investigate hybrid interparticle OAM-based entanglement by exploiting a probabilistic entangling gate. The performance of our approach is assessed by performing quantum state tomography and violating Bell inequalities. Our results pave the way for the use of deterministic sources for the on-demand generation of photonic high-dimensional quantum states.