Abstract Information reconciliation is a significant stage in continuous-variable quantum key distribution (CV-QKD) systems as it directly affects the performance of the CV-QKD systems including secret key rate and secure transmission distance. This paper proposes a multidimensional reconciliation scheme using deep learning in CV-QKD systems. Firstly, different neural networks are constructed to obtain the norm information. Secondly, a multidimensional reconciliation scheme with deep learning assisted norm information is proposed which no longer needs to transmit the norm information through the authenticated classical public channel. Finally, simulation results and performance analysis show that, compared with the traditional multidimensional reconciliation scheme, the multidimensional reconciliation scheme with deep learning assisted norm information can decrease the communication traffic to a certain extent.
Abstract Information reconciliation is a significant stage in continuous-variable quantum key distribution (CV-QKD) systems as it directly affects the performance of the CV-QKD systems including secret key rate and secure transmission distance. This paper proposes a multidimensional reconciliation scheme using deep learning in CV-QKD systems. Firstly, different neural networks are constructed to obtain the norm information. Secondly, a multidimensional reconciliation scheme with deep learning assisted norm information is proposed which no longer needs to transmit the norm information through the authenticated classical public channel. Finally, simulation results and performance analysis show that, compared with the traditional multidimensional reconciliation scheme, the multidimensional reconciliation scheme with deep learning assisted norm information can decrease the communication traffic to a certain extent.
High-speed reconciliation is indispensable for supporting the continuous-variable quantum key distribution (CV-QKD) system to generate the secure key in real-time. However, the error correction process’s high complexity and low processing speed limit the reconciliation speed. Therefore, reconciliation has also become the bottleneck of system performance. In this paper, we proposed a high-speed reconciliation scheme that uses the deep neural network to optimize the decoding process of the low-density parity-check (LDPC) code. We first introduced a network structure of decoding implementation based on the deep neural network, which can be applied to decoding algorithms of parallel strategy and significantly reduce the decoding complexity. Subsequently, we proposed two improved decoding algorithms based on this structure, named linear fitting algorithm and deep neural network-assisted decoding algorithm. Finally, we introduced a high-speed reconciliation scheme based on the CPU-GPU hybrid platform. Simulation results show that the proposed reconciliation scheme reduces the complexity and enables us to realize the high-speed CV-QKD system. Furthermore, the improved decoding algorithm can also reduce the FER, thereby increasing the secret key rate.
Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.
Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. We propose an efficient rate-adaptive reconciliation protocol suitable for practical CV-QKD systems with time-varying quantum channel. This protocol changes the code rate of multi-edge type low density parity check codes, by puncturing (increasing the code rate) and shortening (decreasing the code rate) techniques, to enlarge the correctable signal-to-noise ratios regime, thus improves the overall reconciliation efficiency comparing to the original fixed rate reconciliation protocol. We verify our rate-adaptive reconciliation protocol with three typical code rate, i.e., 0.1, 0.05 and 0.02, the reconciliation efficiency keep around 93.5%, 95.4% and 96.4% for different signal-to-noise ratios, which shows the potential of implementing high-performance CV-QKD systems using single code rate matrix.
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 disclosed data, 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 information disclosure.
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.
Abstract Quantum key distribution (QKD) is a secure cryptographic technology that enables two authenticated parties to share secret keys. Information reconciliation is an essential step in continuous-variable quantum key distribution (CV-QKD) protocols, which affects both the complexity and performance of the system. This paper reviews adaptive reconciliation protocols, and also proposes a new efficient scheme using systematic polar codes. Simulation results show that the proposed scheme can significantly increase reconciliation efficiency and reduce the overall computational complexity by reducing the average number of retransmissions, without significant reduction in effective secret key length.