📝 SummarXiv

Abstract

Here, we present a high-dimensional QKD protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum - selected passively via a 50:50 beamsplitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver (Bob), who similarly performs a random measurement in one of the two basis. This approach combines state preparation and measurement into a single process, eliminating the need for external random number generators. In this proof-of-principle demonstration, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. Looking ahead, we theoretically show that using the same entangled photon source but with next-generation event-based cameras - featuring improved quantum efficiency, timing and spatial resolution - our approach could achieve 10.9 bits per photon at 2500 spatial modes, and a maximum bit rate of 3.1 Mb/s with 5100 modes. This work establishes a scalable path toward high-dimensional, spatially encoded quantum communication with both high photon efficiency and secure bit rates.