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.

翻译：连续变量量子密钥分发（CV-QKD）需要高效的协调技术才能在低信噪比和长距离条件下运行。多维协调通过将物理高斯量子信道转化为虚拟二元输入加性白高斯噪声（BIAWGN）信道来应对这一挑战，从而能够使用现代纠错码。本文回顾了多维协调的原理，重点关注超出代数维度1、2、4、8的高维构造。我们描述了虚拟信道的构建，讨论了用于反向协调的实用编码方案，并分析了它们与线性纠错码的集成。我们还介绍了一个开源仿真框架HDirac，该框架实现了任意维度的多维协调，并利用它评估了最先进的LDPC码。研究结果揭示了维度、协调效率和帧错误率之间的关键权衡，为CV-QKD系统设计提供了实用指导。