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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Recovery of quantum-entanglement after encountering an obstruction

Melanie G. McLaren, Thandeka Mahlanga, Miles J. Padgett, Filippus Stefanus Roux, Andrew Forbes

Published Feb 25, 2014• 0 citations
Publisher

Abstract

Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also o er advantages over other modes in the quantum regime. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. For BG modes, there exists a minimum distance behind an obstruction before reconstruction of the mode occurs. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction moved beyond that minimum distance.

DOI
10.1117/12.2037651

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Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also o er advantages over other modes in the quantum regime. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. For BG modes, there exists a minimum distance behind an obstruction before reconstruction of the mode occurs. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction moved beyond that minimum distance.
Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also offer advantages over other modes in the quantum regime. The easily adjustable radial scale of BG modes provides a more favourable basis of orbital angular momentum (OAM) entanglement over Laguerre- Gaussian (LG) modes, where the radial dependence is often ignored. We demonstrate high-dimensional entanglement with the BG modes and show a higher fidelity than the LG modes. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction was moved beyond that minimum distance.
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.
Summary form only given, as follows. The subject of state reconstruction has recently become a major field of study in quantum optics [see Special issue on Quantum state preparation and measurement, J. Mod Opt., 11/12, (1997), edited by W.P. Schleich and M.G. Raymer]. The quasiprobability functions and density matrices have been measured experimentally for single-mode running fields using the homodyne scheme. However, most of the earlier reconstruction schemes are for single-mode fields. In this presentation the author is interested in reconstruction of a two-mode entangled cavity field.
One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle, both classically and in the quantum regime. Here we demonstrate that the local entanglement, or nonseparability, between the spatial and polarization degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of nonseparability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.
The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.
When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This Letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.