Multidimensional Reconciliation in Continuous-Variable QKD: Review, Coding Schemes, and Open Source Simulation

2026-06-01

AI Summary

This work addresses the information reconciliation bottleneck in continuous-variable quantum key distribution (CV-QKD) under low signal-to-noise ratio and long-distance conditions. The authors propose a multidimensional reverse reconciliation scheme that maps the physical Gaussian quantum channel onto a virtual binary-input additive white Gaussian noise channel, enabling efficient reconciliation through modern linear error-correcting codes such as LDPC codes. Breaking conventional dimensional constraints, the study systematically investigates reconciliation performance across arbitrary algebraic dimensions beyond eight for the first time, quantifying the trade-offs among dimensionality, reconciliation efficiency, and frame error rate. The open-source simulation framework HDircac, released alongside this work, offers flexible evaluation capabilities and provides practical guidance and technical support for CV-QKD system design.

Abstract

Continuous-variable quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.

Problem

• continuous-variable quantum key distribution
• multidimensional reconciliation
• low signal-to-noise ratio
• long-distance QKD
• BIAWGN channel

Innovation

• multidimensional reconciliation
• continuous-variable QKD
• BIAWGN channel
• LDPC codes
• open-source simulation