# Asymptotic security of continuous-variable quantum key distribution with a discrete modulation

## TL;DR

This paper derives a lower bound on the secret key rate for continuous-variable quantum key distribution with discrete modulation, demonstrating feasibility over long distances and advancing security proofs for practical quantum communication.

## Contribution

It introduces a semidefinite programming approach to establish asymptotic security bounds for discrete-modulated CV-QKD, including QPSK and QAM schemes.

## Key findings

- Achieves over 100 km secure communication distance with realistic noise levels.
- Provides a general framework for security analysis of discrete modulation schemes.
- Paves the way for large-scale deployment of CV-QKD protocols.

## Abstract

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.