Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation

TL;DR

This paper derives an analytical lower bound on the asymptotic secret key rate for continuous-variable quantum key distribution with arbitrary modulation, enabling better understanding and practical implementation of secure quantum communication.

Contribution

It provides the first analytical lower bound for arbitrary modulation in CV-QKD, extending beyond Gaussian and simple phase-shift keying protocols, and shows small constellations are nearly optimal.

Findings

Analytical bound matches previous numerical results.

Small constellations (e.g., 64 states) are nearly optimal.

Bounds applicable to arbitrary states, not just pure states.

Abstract

We establish an analytical lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation of coherent states. Previously, such bounds were only available for protocols with a Gaussian modulation, and numerical bounds existed in the case of simple phase-shift-keying modulations. The latter bounds were obtained as a solution of convex optimization problems and our new analytical bound matches the results of Ghorai et al. (2019), up to numerical precision. The more relevant case of quadrature amplitude modulation (QAM) could not be analyzed with the previous techniques, due to their large number of coherent states. Our bound shows that relatively small constellation sizes, with say 64 states, are essentially sufficient to obtain a performance close to a true Gaussian modulation and are therefore an attractive solution for large-scale deployment of continuous-variable quantum key distribution. We also derive similar bounds when the modulation consists of arbitrary states, not necessarily pure.