# Numerical simulation of the optimal two-mode attacks for two-way continuous-variable quantum cryptography in reverse reconciliation

## TL;DR

This paper derives the secret key rates for two-way continuous-variable quantum key distribution under all accessible two-mode attacks, identifying the optimal attack and demonstrating the protocol's advantage over one-way methods for long-distance secure communication.

## Contribution

It provides a comprehensive analysis of the security against all accessible two-mode attacks and identifies the optimal attack model for the two-way protocol.

## Key findings

- Optimal two-mode attack minimizes secret key rates and transmission distances.
- Two-way protocol outperforms one-way protocol even under optimal attack.
- The analysis demonstrates the potential for long-distance secure quantum communication.

## Abstract

We analyze the security of the two-way continuous-variable quantum key distribution protocol in reverse reconciliation against general two-mode attacks, which represent all accessible attacks at fixed channel parameters. Rather than against one specific attack model, the expression of secret key rates of the two-way protocol are derived against all accessible attack models. It is found that there is an optimal two-mode attack to minimize the performance of the protocol in terms of both secret key rates and maximal transmission distances. We identify the optimal two-mode attack, give the specific attack model of the optimal two-mode attack and show the performance of the two-way protocol against the optimal two-mode attack. Even under the optimal two-mode attack, the performances of two-way protocol are still better than the corresponding one-way protocol, which shows the advantage of making a double use of the quantum channel and the potential of long-distance secure communication using two-way protocol.