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arXiv:quant-ph/0303003

Concentration of higher dimensional entanglement

Alipasha Vaziri, Jian-Wei Pan, Thomas D. Jennewein, Gregor Weihs, Anton Zeilinger

Published Mar 1, 2003• 4 citations
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Abstract

Enhancement of entanglement enhancement is necessary for most quantum communication protocols many of which are defined in Hilbert spaces larger than two. In this work we present the experimental realization of entanglement concentration of orbital angular momentum entangled photons produced in the spontaneous parametric down-conversion process which have been shown to provide a source for higher dimensional entanglement. We investigate the specific case of three dimensions and the possibility of generating different entangled states out of an initial state. The results presented here are of importance for pure states as well as for mixed states.

DOI
10.48550/arxiv.quant-ph/0303003

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Enhancement of entanglement enhancement is necessary for most quantum communication protocols many of which are defined in Hilbert spaces larger than two. In this work we present the experimental realization of entanglement concentration of orbital angular momentum entangled photons produced in the spontaneous parametric down-conversion process which have been shown to provide a source for higher dimensional entanglement. We investigate the specific case of three dimensions and the possibility of generating different entangled states out of an initial state. The results presented here are of importance for pure states as well as for mixed states.
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.
Orbital angular momentum entangled photons emitted by a down-conversion source are in higher dimensional entangled states. Here we report the experimental confirmation by demonstrating a violation of a generalized Clauser-Horne-Shimony-Holt-type Bell inequality in three dimensions by more than 18 standard deviations. Higher dimensional entangled states allow the realization of new types of quantum communication protocols. They also provide a more secure quantum cryptography scheme. Therefore our experimental results are likely to have applications in future quantum communication technology.
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.
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.