Entanglement of the properties of two separated particles constitutes<br />a fundamental signature of quantum mechanics and is a key resource<br />for quantum information science. We demonstrate strong Einstein,<br />Podolsky, and Rosen correlations between the angular position and<br />orbital angular momentum of two photons created by the nonlinear<br />optical process of spontaneous parametric down-conversion. The discrete<br />nature of orbital angular momentum and the continuous but periodic<br />nature of angular position give rise to a special sort of entanglement<br />between these two variables. The resulting correlations are found<br />to be an order of magnitude stronger than those allowed by the uncertainty<br />principle for independent (nonentangled) particles. Our results suggest<br />that angular position and orbital angular momentum may find important<br />applications in quantum information science.
Leach, J., Jack, B., Romero, J., Jha, A. K., Yao, A. M., Franke-Arnold, S., … Padgett, M. J. (2010). Quantum correlations in optical angle-orbital angular momentum variables. Science, 329(5992), 662–665. https://doi.org/10.1126/science.1190523