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South African Journal of Science

Realising high-dimensional quantum entanglement with orbital angular momentu

Melanie G. McLaren, Filippus Stefanus Roux, Andrew Forbes

Published Jan 29, 2015• 10 citations
Publisher

Abstract

We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair were investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states were examined in detail and we show high-dimensional entanglement in a Hilbert space of dimension 25. High-dimensional entanglement introduces the possibility for more secure communication and more efficient computations. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.

DOI
10.17159/sajs.2015/20130322

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Realising high-dimensional quantum entanglement with orbital angular momentum

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We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair are investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states are examined in detail, where we show high-dimensional entanglement in a Hilbert space of dimension 25. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.

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We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair were investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states were examined in detail and we show high-dimensional entanglement in a Hilbert space of dimension 25. High-dimensional entanglement introduces the possibility for more secure communication and more efficient computations. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.
We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair are investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states are examined in detail, where we show high-dimensional entanglement in a Hilbert space of dimension 25. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
Quantum entanglement is a fundamental trait of quantum mechanics that causes the information about the properties of two (or more) objects to be inextricably linked. When a measurement on one of the objects is performed, the state of the other object is immediately altered, even when these objects are separated at arbitrary distances. In this thesis, we explore the rich properties of entanglement in a high-dimensional mode space. Experimentally, we have implemented the high dimensionality by use of the orbital-angular-momentum degree of freedom of entangled photon pairs. The emphasis is on the question how to quantify the dimensionality of the entanglement as measured in an experiment. We introduce the Shannon dimensionality as a useful quantifier of measured entanglement. Furthermore, we discuss various production methods of optical phase plates, which we use to manipulate the orbital-angular-momentum states of light. Finally, we present an experimental feasibility study on the potential of orbital-angular-momentum entanglement for free-space quantum communication through the atmosphere
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
Entangled quantum states in high-dimensional space show many advantages compared with entangled states in two-dimensional space. The former enable quantum communication with higher channel capacity, enable more efficient quantum-information processing and are more feasible for closing the detection loophole in Bell test experiments. Establishing high-dimensional entangled memories is essential for long-distance communication, but its experimental realization is lacking. We experimentally established high-dimensional entanglement in orbital angular momentum space between two atomic ensembles separated by 1 m. We reconstructed the density matrix for a three-dimensional entanglement and obtained an entanglement fidelity of (83.9±2.9)%. More importantly, we confirmed the successful preparation of a state entangled in more than three-dimensional space (up to seven-dimensional) using entanglement witnesses. Achieving high-dimensional entanglement represents a significant step toward a high-capacity quantum network.