Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration

TL;DR

This paper provides a detailed security analysis of a continuous-variable quantum cryptography protocol with an untrusted relay, demonstrating that two-mode coherent attacks are optimal and outperform simpler attack strategies.

Contribution

It offers a comprehensive security analysis of the symmetric configuration, identifying the optimal eavesdropping strategies and their impact on security thresholds and key rates.

Findings

Two-mode coherent attacks outperform one-mode collective attacks.

Optimal attacks depend on transmissivity and thermal noise.

Security thresholds are affected by the type of eavesdropping strategy.

Abstract

We consider the continuous-variable protocol of Pirandola et al. [Nature Photonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strategies against the quantum links explicitly showing that, at fixed transmissivity and thermal noise, two-mode coherent attacks are optimal, manifestly outperforming one-mode collective attacks based on independent entangling cloners. Such an advantage is shown both in terms of security threshold and secret-key rate.