Twin-Field Quantum Key Distribution with Fully Discrete Phase Randomization

Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them already implemented experimentally. Most assume that the users emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close loophole, we propose prove variant relies exclusively discrete phase randomisation. Remarkably, our results show it also provide higher secret-key rates counterpart protocols rely