Finite-key analysis for quantum key distribution with discrete phase randomization

TL;DR

This paper presents a finite-key security analysis for twin-field quantum key distribution using discrete phase randomization, demonstrating its practicality and extending security proofs to this realistic scenario.

Contribution

It provides the first finite-key security proof for TF-QKD with discrete phase randomization, introducing a novel analysis technique applicable to various QKD protocols.

Findings

Discrete phase randomization with 8 phases achieves satisfactory performance.

The proposed method extends security proofs to realistic experimental conditions.

TF-QKD can be secure with finite keys using discrete phase choices.

Abstract

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 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 key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete phase-randomization instead of continuous one. However, a security proof for a QKD protocol with discrete phase-randomization in finite-key region is still missing. Here we develop a technique based on conjugate measurement and quantum state distinguishment to ana-lyze the security in this case. Our result shows that TF-QKD with reasonable number of discrete random phases, e.g. 8 phases from {0, pi/4, pi/2, ..., 7pi/4}, can achieve satisfactory performance. More importantly, as a the first proof for TF-QKD with discrete phase-randomization in finite-key region, our method is also applicable in other QKD protocols.