Sending-or-not-sending twin-filed quantum key distribution with discrete phase modulation

TL;DR

This paper analyzes the security and performance of a discrete phase modulation variant of the sending-or-not-sending quantum key distribution protocol, demonstrating that limited phase values can surpass linear bounds and approach continuous modulation performance.

Contribution

The paper provides the first security proof and analytic key rate formulas for the SNS protocol with discrete phase modulation, including numerical simulations showing its effectiveness.

Findings

Key rates exceed linear bounds with 6 phase values.

Key rates approach continuous modulation results with 12 phase values.

Discrete phase modulation can be practically effective for QKD.

Abstract

We study the sending-or-not-sending (SNS) protocol with discrete phase modulation of coherent states. We first make the security of the SNS protocol with discrete phase modulation. We then present analytic formulas for key rate calculation. We take numerical simulations for the key rate through discrete phase modulation of both the original SNS protocol and the SNS protocol with two way classical communications of active-odd-parity pairing (AOPP). Our numerical simulation results show that only with $6$ phase values, the key rates of the SNS protocol can exceed the linear bound, and with $12$ phase values, the key rates are very close to the results of the SNS protocol with continuously modulated phase-randomization.