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Abstract
The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum correlations for the conjugate variables of orbital angular momentum and angular position. We determine an experimentally testable criterion for the demonstration of an angular version of the EPR paradox. For the interpretation of future experimental results from our proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. For this measurement angular apertures are used to determine the probability density of the angle. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected.
Acknowledgments
We would like to thank Roberta Zambrini for useful discussions and for the suggestion to use truncated super Gaussians. Also, Eric Yao and Miles Padgett have been very helpful with questions regarding the experimental implementation. This work has received support from the Engineering and Physical Sciences Research Council (EPSRC) under grant GR S03898/01 and the Royal Society of Edinburgh.