Scheme for optical implementation of orbital angular momentum beam splitter of a light beam and its application in quantum information processing

Optical beams bearing orbital angular momentum have been recently recognized as potential candidates for realizing D-dimensional quantum systems (qudits). In this paper, we propose an optical scheme to implement an orbital angular momentum beam splitter, which changes the outgoing direction with respect to the incoming direction while leaving the qudit state unchanged. Furthermore we demonstrate that such a beam splitter can be used to sort different orbital angular states of a single photon, create arbitrary superpositions of orbital angular momentum states, and implement a high-dimensional Bennett-Brassard 1984 protocol for quantum key distribution.