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Laser Physics Letters

High-dimensional entanglement concentration of twisted photon pairs

L X Chen, Qingyuan Wu

Published Aug 7, 2012• 6 citations
Publisher

Abstract

Recently, Dada et al. reported on the experimental entanglement concentration and violation of generalized Bell inequalities with orbital angular momentum (OAM) [Nat. Phys. 7 , 677 (2011)]. Here we demonstrate that the high-dimensional entanglement concentration can be performed in arbitrary OAM subspaces with selectivity. Instead of violating the generalized Bell inequalities, the working principle of present entanglement concentration is visualized by the biphoton OAM Klyshko picture, and its good performance is confirmed and quantified through the experimental Shannon dimensionalities after concentration.

DOI
10.7452/lapl.201210066

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Recently, Dada et al. reported on the experimental entanglement concentration and violation of generalized Bell inequalities with orbital angular momentum (OAM) [Nat. Phys. 7 , 677 (2011)]. Here we demonstrate that the high-dimensional entanglement concentration can be performed in arbitrary OAM subspaces with selectivity. Instead of violating the generalized Bell inequalities, the working principle of present entanglement concentration is visualized by the biphoton OAM Klyshko picture, and its good performance is confirmed and quantified through the experimental Shannon dimensionalities after concentration.
Twisted photons enable the definition of a Hilbert space beyond two dimensions by orbital angular momentum (OAM) eigenstates. Here we propose a feasible entanglement concentration experiment, to enhance the quality of high-dimensional entanglement shared by twisted photon pairs. Our approach is started from the full characterization of entangled spiral bandwidth, and is then based on the careful selection of the Laguerre–Gaussian (LG) modes with specific radial and azimuthal indices p and l. In particular, we demonstrate the possibility of high-dimensional entanglement concentration residing in the OAM subspace of up to 21 dimensions. By means of LabVIEW simulations with spatial light modulators, we show that the Shannon dimensionality could be employed to quantify the quality of the present concentration. Our scheme holds promise in quantum information applications defined in high-dimensional Hilbert space.
Orbital angular momentum entangled photons emitted by a down-conversion source are shown to be in higher dimensional entangled states. This is experimentally confirmed by demonstrating a violation of Clauser-Horne-Shimony-Holt-type Bell inequalities. The experiment is performed in two steps. First, the two-photon two-dimensional entanglement is demonstrated for orbital angular momentum states by violating the usual CHSH Bell inequality. In a second step the setup is extended in order to show that the entanglement also holds in three dimensions. By using a generalized type of the CHSH Bell inequality, a violation of more than 18 standard deviations is achieved. Higher dimensional entangled states thus allow the realization of new types of quantum communication protocols. They also provide a more secure quantum cryptography scheme.
High-dimensional entanglement is a valuable resource for quantum communication, and photon pairs entangled in orbital angular momentum (OAM) are commonly used for encoding high-dimensional quantum states. However, methods for the preparation of maximally entangled states of arbitrary dimensionality are still lacking, and currently used approaches essentially rely on filtering and entanglement concentration. Here, we experimentally realize a method for the generation of high-dimensional maximally entangled OAM states of photon pairs which does not require any of these procedures. Moreover, the prepared state is restricted to the subspace of the specified dimensionality, thus requiring minimal spatial postselection.
Entanglement in higher dimensions is an attractive concept that is a chal- lenge to realise experimentally. To this end, the entanglement of the orbital angular momentum (OAM) of photons holds promise. The OAM state-space is discrete and theoretically unbounded. In the work that follows, we investi- gate various aspects of OAM entanglement. We show how the correlations in OAM and its conjugate variable, angular position, are determined by phase- matching and the shape of the pump beam in spontaneous parametric down- conversion. We implement tests of quantum mechanics which have been previously done for other variables. We show the Einstein-Podolsky-Rosen paradox for OAM and angle, supporting the incompatibility of quantum me- chanics with locality and realism. We demonstrate violations of Bell-type inequalities, thereby discounting local hidden variables for describing the correlations we observe. We show the Hardy paradox using OAM, again highlighting the nonlocal nature of quantum mechanics. We demonstrate violations of Leggett-type inequalities, thereby discounting nonlocal hidden variables for describing correlations. Lastly, we have looked into the entan- glement of topological vortex structures formed from a special superposition of OAM modes and show violations of Bell-type inequalities confined to a finite, isolated volume.
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.