Joint parameter estimation and multidimensional reconciliation for continuous-variable quantum key distribution

TL;DR

The paper tackles pilot overhead and error propagation in continuous-variable quantum key distribution by introducing a joint Bayesian framework that merges channel parameter estimation with multidimensional reconciliation. It uses an EM algorithm within a factor-graph-based generalized sum-product message passing scheme to learn the channel parameters ($t$ and $\sigma^2$) while decoding via LDPC codes. A novel hybrid multidimensional rotation further reduces classical-channel feedback. Simulations show the approach achieves superior parameter estimation and reconciliation efficiency, approaching the performance of exhaustive ML with substantially fewer pilots, signaling a practical path to high-efficiency CV-QKD.

Abstract

Accurate quantum channel parameter estimation is essential for effective information reconciliation in continuous-variable quantum key distribution (CV-QKD). However, conventional maximum likelihood (ML) estimators rely on a large amount of discarded data (or pilot symbols), leading to a significant loss in symbol efficiency. Moreover, the separation between the estimation and reconciliation phases can introduce error propagation. In this paper, we propose a novel joint message-passing scheme that unifies channel parameter estimation and information reconciliation within a Bayesian framework. By leveraging the expectation-maximization (EM) algorithm, the proposed method simultaneously estimates unknown parameters during decoding, eliminating the need for separate ML estimation. Furthermore, we introduce a hybrid multidimensional rotation scheme that removes the requirement for norm feedback, significantly reducing classical channel overhead. To the best of our knowledge, this is the first work to unify multidimensional reconciliation and channel parameter estimation in CV-QKD, providing a practical solution for high-efficiency reconciliation with minimal pilots.

Figures (6)

• Figure 1: Illustration of the factor graph used for message passing in the proposed joint parameter estimation and information reconciliation scheme. Variable nodes are represented by blank circles, and factor nodes by black squares.
• Figure 2: RMSE of parameter estimation versus SNR for an ATSC 3.0 LDPC code with rate $R=0.2$. a) RMSE for estimating $t$; and b) RMSE for estimating $\sigma^2$.
• Figure 3: BER and FER for an ATSC 3.0 LDPC code with rate $R=0.2$. a) BER versus SNR; and b) FER versus $\beta$.
• Figure 4: BER and FER for an ATSC 3.0 LDPC code with rate $R=0.1333$. a) BER versus SNR; and b) FER versus $\beta$.
• Figure 5: BER and FER performance versus the number of pilots for different reconciliation dimensions and efficiencies. a) BER; and b) FER.