A simple proof that Gaussian attacks are optimal among collective attacks against continuous-variable quantum key distribution with a Gaussian modulation

TL;DR

This paper provides a straightforward proof demonstrating that Gaussian attacks are optimal among collective attacks in continuous-variable quantum key distribution with Gaussian modulation, leveraging symmetry properties in phase-space.

Contribution

The paper introduces a simple, symmetry-based proof confirming the optimality of Gaussian attacks in a specific quantum key distribution setting.

Findings

Gaussian attacks are proven to be optimal among collective attacks.

The proof relies on symmetry properties in phase-space.

The result simplifies security analysis for CV-QKD protocols.

Abstract

In this paper, we give a simple proof of the fact that the optimal collective attacks against continous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof makes use of symmetry properties of the quantum key distribution protocol in phase-space.