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Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces

Leach, J. and Jack, B. and Romero, J. and Ritsch-Marte, M. and Boyd, R.W. and Jha, A.K. and Barnett, S.M. and Franke-Arnold, S. and Padgett, M.J. (2009) Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces. Optics Express, 17 (10). pp. 8287-8293. ISSN 1094-4087

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We observe entanglement between photons in controlled super-position states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality. We demonstrate this violation in a number of two-dimensional subspaces of the higher dimensional OAM Hilbert space.