Finite-Key Analysis for Quantum Key Distribution with Discrete-Phase Randomization

Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2 pi, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,pi/4,pi/2, horizontal ellipsis ,7 pi/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.

Automated summary

Quantum key distribution (QKD) allows secure sharing of keys between remote parties. Continuous phase randomization, commonly assumed in QKD protocols, is challenged in experiments. In this study, we propose a technique based on conjugate measurement and quantum state distinguishment to analyze the security of a QKD protocol with discrete-phase randomization. Our results show that TF-QKD with a reasonable number of discrete random phases can achieve satisfactory performance, but finite-size effects become more notable. This method is also applicable to other QKD protocols.