Spatial-Mode Quantum Cryptography in a 545-Dimensional Hilbert Space

Abstract: A major challenge in quantum key distribution (QKD) with spatial modes lies in efficiently generating, manipulating, and detecting high-dimensional quantum states. Here, we present a hybrid QKD protocol that integrates entanglement-based and prepare-and-measure approaches, utilizing position and momentum correlations of photon pairs generated via spontaneous parametric downconversion. Through projective measurements on one photon, the sender remotely prepares spatial modes at the receiver's end, simplifying state preparation. Detection is enhanced using advanced event-based single-photon cameras. Our scheme supports QKD in a 545-dimensional Hilbert space-the highest reported for spatial encoding-achieving 5.07 bits per coincidence in an optimized 90-mode configuration. This work demonstrates a scalable route to high-dimensional, spatially encoded quantum communication.