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Physical Review A

Nonlocality of high-dimensional two-photon orbital angular momentum states

Andrea Aiello, Sumant S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman

Published Nov 30, 2005• 45 citations
Publisher

Abstract

We propose an interferometric method to investigate the nonlocality of high-dimensional two-photon orbital angular momentum states generated by spontaneous parametric down conversion. We incorporate two half-integer spiral phase plates and a variable-reflectivity output beam splitter into a Mach-Zehnder interferometer to build an orbital angular momentum analyzer. This setup enables testing the nonlocality of high-dimensional two-photon states by repeated use of the Clauser-Horne-Shimony-Holt inequality.

DOI
10.1103/physreva.72.052114

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We propose an interferometric method to investigate the nonlocality of high-dimensional two-photon orbital angular momentum states generated by spontaneous parametric down conversion. We incorporate two half-integer spiral phase plates and a variable-reflectivity output beam splitter into a Mach-Zehnder interferometer to build an orbital angular momentum analyzer. This setup enables testing the nonlocality of high-dimensional two-photon states by repeated use of the Clauser-Horne-Shimony-Holt inequality.
We propose a novel setup to investigate the quantum non-locality of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate non-integer spiral phase plates in spatial analyzers, enabling us to use only two detectors. The resulting setup is somewhat reminiscent of that used to measure polarization entanglement. However, the two-photon states that are produced, are not confined to a 2X2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict a violation of the Clauser-Horne-Shimony-Holt version of the Bell inequality (S<=2), that is even stronger than achievable for two qubits (S=2*(2^1/2)), namely S=16/5
We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a 2 x 2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict that the Clauser-Horne-Shimony-Holt-Bell parameter S is larger than achievable for two qubits (S=2 sqrt[2]), namely, S=31 / 5.
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.