Optimizing the qudit dimensions of position-momentum entangled photons for quantum key distribution

We propose an optimization scheme to maximize the secure key rate of a high-dimensional variant of BBM92. We use the position-momentum conjugate bases to encode the higher-dimensional qudits realized in a fully passive optical setup. The setup employs a single lens for the basis measurements and no lossy or slow elements. We optimize the qudit dimension for the protocol by maximizing the number of equiprobable sections (macropixels) of the detected beam while minimizing their overlap error. We show the enhanced key rate by discarding events from the ambiguous border pixels. Our strategy maximizes the overlap between the discarded regions from neighboring macropixels, thereby globally minimizing the overall loss and error. We calculate the optimal dimension and the secure key rate for certain beam parameters. We experimentally show the feasibility of our scheme. This work paves the way for realistic implementations of high-dimensional device-independent quantum key distribution with enhanced bit rates.