In multidimensional reconciliation (MR) of continuous-variable quantum key distribution (CV-QKD) systems, the performance of conventional schemes is often limited by unreliable Gaussian-modulated coherent states (GMCSs). In this paper, we propose a reliability-driven preprocessing framework for MR. The proposed framework introduces a multi-step sample interleaver that redistributes GMCSs to increase intra-vector reliability while reducing the reliability imbalance across vectors. In addition, a bit-allocation strategy is designed to align the reliability of the soft information generated by MR with the reliability requirements of the employed forward error correction (FEC) codes. To further reduce implementation overhead, simplified log-likelihood ratio (LLR) estimation methods are also investigated. Simulation results demonstrate that the proposed scheme significantly improves the frame error rate (FER) performance compared with conventional schemes, while introducing only negligible additional latency, thereby extending the achievable transmission distance of CV-QKD systems.
In multidimensional reconciliation (MR) of continuous-variable quantum key distribution (CV-QKD) systems, the performance of conventional schemes is often limited by unreliable Gaussian-modulated coherent states (GMCSs). In this paper, we propose a reliability-driven preprocessing framework for MR. The proposed framework introduces a multi-step sample interleaver that redistributes GMCSs to increase intra-vector reliability while reducing the reliability imbalance across vectors. In addition, a bit-allocation strategy is designed to align the reliability of the soft information generated by MR with the reliability requirements of the employed forward error correction (FEC) codes. To further reduce implementation overhead, simplified log-likelihood ratio (LLR) estimation methods are also investigated. Simulation results demonstrate that the proposed scheme significantly improves the frame error rate (FER) performance compared with conventional schemes, while introducing only negligible additional latency, thereby extending the achievable transmission distance of CV-QKD systems.
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.
Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV QKD). For Gaussian-modulated coherent-state CV QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multiedge-type low-density parity-check codes (MET LDPC) are used in a non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error-correction performance of Gaussian data and non-Gaussian data. The results show that the error-correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50 % for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25 %.
Continuous variable quantum key distribution (CV-QKD) enables authenticated parties to share a key. Information reconciliation (IR) is a critical step of the post-processing in CV-QKD, significantly affecting the secret key rate (SKR) shared between the legitimate parties. To improve the SKR performance of the CV-QKD without increasing the key inconsistency rate (KIR), this paper proposes a twofold IR method by performing independent operations on the Gaussian modulated coherent states (GMCS) obtained over the quantum channel. Specifically, assuming reverse reconciliation, after the GMCS are quantized, Bob generates parity bits, which are shared with Alice to help her correct the inconsistent bits in the quantized bits to generate the partial key. At the same time, the parity bits are used as frozen bits of polar codes in the multidimensional reconciliation (MR) to generate the other partial key. Simulation results demonstrate that the proposed twofold IR method increases the SKR nearly twice without increasing the inconsistent bits. In addition, we propose to apply symbol expansion and rotation (SER) based on the mapped GMCS to reduce the amount of information to be transmitted over the public error-free channel. Simulation results demonstrate that the performance of the proposed twofold IR with SER method can achieve a higher SKR with 3dB performance gap to that of the traditional MR protocol.
Information reconciliation is a crucial process in continuous-variable quantum key distribution(CV-QKD) systems. The slice error correction (SEC) reconciliation is appropriate for short-distance CV-QKD. However, the efficiency of SEC reconciliation schemes is significantly influenced by noisy channels with low signal-to-noise ratios (SNRs). In this paper, we present an enhanced information reconciliation scheme, termed AC-SEC reconciliation, which adds the new Gaussian sequences c with the original Gaussian sequences y before quantization in the SEC reconciliation to obtain secret key sequences with high variance and reduce noise interferences. Simulation results demonstrate that compared with the traditional SEC reconciliation, the proposed information reconciliation has lower frame error rate (FER) and higher reconciliation efficiency, which can increase the secret key rate (SKR).
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
For continuous variable quantum key distribution (CV-QKD) protocol, information reconciliation (IR) is a key step that can significantly affect the performance of CV-QKD. Because of multidimensional reconciliation suitable for low signal-to-noise ratio (SNR) and long transmission distance scenario, a parallel architecture for the multidimensional reconciliation in CV-QKD implemented on field programmable gate array (FPGA) is proposed in this paper. Using a binarized d-dimensional spherical vector c and a parallel computation of the coefficient a and rotation matrix M, the parallel architecture achieves 45.635 Mbps processing throughput at 250 MHz in the system clock, with frame error rate (FER) less than 0.001 when the SNR exceeds 0.71 dB.