# Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution

## TL;DR

This paper presents a numerical security analysis of discrete-modulation CV QKD protocols, demonstrating their potential for higher key rates and longer distances compared to previous schemes, with versatile evaluation methods.

## Contribution

It introduces a general numerical method for analyzing discrete-modulation CV QKD security, focusing on quaternary modulation, and shows improved key rates and distances over prior binary and ternary schemes.

## Key findings

- Higher key rates over longer distances with quaternary modulation
- Versatile security analysis applicable to protocol variations
- Postselection and reverse reconciliation improve key rates

## Abstract

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.