Finite-size general security for relativistic phase shift keying via variable-length quantum key distribution

Differential phase shift keying constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by considering an alternative scheme, herewith denominated relativistic phase shift keying (RPSK). We leverage variable-length general security techniques via entropy accumulation, together with methods based on Rényi leftover hashing and conic optimization. Our approach achieves secret key rates with ${10}^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of RPSK.