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

Abstract

Differential phase shift keying (DPSK) constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances in the security of DPSK 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 leveraging recent techniques in variable-length general security by using entropy accumulation techniques based on R\'enyi leftover hashing, together with conic optimization methods. Our approach achieves secret key rates with $10^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of industrial-grade DPSK.