Secure information capacity of photons entangled in many dimensions

We quantify precisely the maximum secure information capacity of photons entangled in high dimensions for entanglement in the orbital angular momentum and angular degrees of freedom. Our analysis takes careful account of the influence of experimental imperfections, such as nonunity detection efficiency, on the degree of Einstein-Podolsky-Rosen (EPR) entanglement and hence on the secure information capacity of the photon pairs. We find that there is is an optimal dimension that maximizes the secure information capacity whose value can be predicted analytically from the knowledge of only a few experimental parameters.