# Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks

## TL;DR

This paper provides a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution, demonstrating its potential for high-rate secure communication over metropolitan distances even against the most general attacks.

## Contribution

It extends security proofs for CV MDI QKD to finite-size scenarios against coherent attacks, improving secret key rate estimates with new theoretical tools.

## Key findings

- CV MDI QKD can achieve nonzero secret key rates after 10^7-10^9 signals
- The protocol is secure against the most general coherent attacks in finite-size regimes
- High key rates are feasible on metropolitan scales despite loss and noise

## Abstract

We present a rigorous security analysis of Continuous-Variable Measurement-Device Independent Quantum Key Distribution (CV MDI QKD) in a finite size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with new findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after 10^7-10^9 quantum signal transmissions, depending on loss and noise, and on the required level of security.