Quantum key distribution with non-ideal heterodyne detection: composable security of discrete-modulation continuous-variable protocols

TL;DR

This paper develops a rigorous security proof for discrete-modulation continuous-variable quantum key distribution using realistic heterodyne detection, accounting for device imperfections and establishing composable security in finite-size regimes.

Contribution

It introduces a novel security analysis that incorporates non-ideal heterodyne detection and proves composable security for discrete-modulation protocols in finite-size settings.

Findings

First security proof for discrete-modulation CV-QKD with realistic heterodyne detection.

Establishes composable security in finite-size regime.

Provides tight key rate bounds via semi-definite programming.

Abstract

Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security proofs developed so far relied on idealised mathematical models for such measurements, which assume that the measurement outcomes are continuous and unbounded variables. As physical measurement devices have finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the actual experimental implementations. However, a quantitative analysis of the error introduced by this approximation, and of its impact on composable security, have been lacking so far. Here we present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We focus on collective attacks, and present security proofs for the asymptotic and finite-size regimes, the latter within the framework of composable security. In doing this, we establish for the first time the composable security of discrete-modulation continuous-variable quantum key distribution in the finite-size regime. Tight bounds on the key rates are obtained through semi-definite programming and do not rely on a truncation of the Hilbert space.