Two-way Gaussian quantum cryptography against coherent attacks in direct reconciliation

TL;DR

This paper analyzes the security of a two-way Gaussian quantum cryptography protocol under coherent attacks, providing analytical keyrate expressions and identifying the most effective eavesdropping strategies.

Contribution

It offers a detailed security analysis with a general analytical keyrate formula considering two-mode coherent attacks in two-way quantum communication.

Findings

Residual two-mode correlations impact security

Optimal eavesdropping is a symmetric, separable two-mode attack

Analytical expression for keyrate under coherent attacks

Abstract

We consider the two-way quantum cryptographic protocol with coherent states assuming direct reconciliation. A detailed security analysis is performed considering a two-mode coherent attack, that represents the residual eavesdropping once the parties have reduced the general attack by applying symmetric random permutations. In this context we provide a general analytical expression for the keyrate, discussing the impact of the residual two-mode correlations on the security of the scheme. In particular we identify the optimal eavesdropping against two-way quantum communication, which is given by a two-mode coherent attack with symmetric and separable correlations.