Continuous-variable quantum key distribution (CV-QKD) relies on efficient information reconciliation to establish identical secret key sequences from correlated modulation data and measurement outcomes. Accurate quadrature measurements are essential for reliable reconciliation, but residual phase mismatch between the signal and local oscillator distorts these measurements in coherent receivers and degrades decoding performance. To improve robustness against residual phase mismatch in homodyne-based CV-QKD, we propose a phase-aware multidimensional reconciliation method that jointly performs syndrome-based low-density parity-check (LDPC) decoding and expectation-maximization-based residual-phase refinement. We derive a discrete-time detection model that explicitly incorporates the receiver’s pulse-dependent quadrature-selection phase and construct phase-dependent virtual observations through multidimensional orthogonal mapping. The LDPC decoder provides posterior information for calculating the posterior spherical-symbol moments used in residual-phase refinement, while the refined phase is fed back to update the virtual observations and decoding likelihoods for the next iteration. Numerical results show that the proposed method achieves a lower residual-phase-estimation RMSE than disclosure-based cross-correlation estimation, BER and FER close to those under perfect phase compensation, and a higher finite-size secret key rate.
Continuous-variable quantum key distribution (CV-QKD) relies on efficient information reconciliation to establish identical secret key sequences from correlated modulation data and measurement outcomes. Accurate quadrature measurements are essential for reliable reconciliation, but residual phase mismatch between the signal and local oscillator distorts these measurements in coherent receivers and degrades decoding performance. To improve robustness against residual phase mismatch in homodyne-based CV-QKD, we propose a phase-aware multidimensional reconciliation method that jointly performs syndrome-based low-density parity-check (LDPC) decoding and expectation-maximization-based residual-phase refinement. We derive a discrete-time detection model that explicitly incorporates the receiver’s pulse-dependent quadrature-selection phase and construct phase-dependent virtual observations through multidimensional orthogonal mapping. The LDPC decoder provides posterior information for calculating the posterior spherical-symbol moments used in residual-phase refinement, while the refined phase is fed back to update the virtual observations and decoding likelihoods for the next iteration. Numerical results show that the proposed method achieves a lower residual-phase-estimation RMSE than disclosure-based cross-correlation estimation, BER and FER close to those under perfect phase compensation, and a higher finite-size secret key rate.
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.
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.
The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses d-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's t-distribution. Therefore, we propose a t-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed t-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.
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 %.
In continuous-variable (CV) quantum key distribution (QKD), the reconciliation efficiency and frame error rate of the information reconciliation have a significant impact on the secret key rate. For a fixed-rate multiedge-type low-density parity-check (LDPC) code, the reconciliation efficiency and frame error rate will inevitably vary due to the fluctuations of the signal-to-noise ratio (SNR) of the CV QKD system, which degrades the performance of the system. We propose a high-efficiency rate-adaptive information reconciliation scheme by combining raptorlike (RL) LDPC codes with the addition of trusted noises. We establish the model of adding trusted noises and combine it with the RL LDPC codes to optimize the secret key rate under the time-varying channel. The simulation results show that our scheme can maintain a high reconciliation efficiency of more than 94.4% and a low frame error rate within 15% fluctuation range of the SNR. Furthermore, we implement the hardware acceleration of the proposed rate-adaptive scheme on a graphics processing unit and achieve a decoding throughput of 65.5 Mbits/s by optimizing the storage of the parity-check matrix. Our results are useful for the practical CV QKD under the realistic time-varying channel.
In order to ensure the security of the local oscillator (LO) in continuous variable quantum key distribution (CV-QKD), the LO in CV-QKD based on the local LO (LLO) scheme no longer passes through the quantum channel. For the LLO scheme using homodyne detection, two orthogonal quadratures of reference pulse can only be measured sequentially, which, as a result, each signal pulse should be accompanied by a pair of identical reference pulses. However, due to the phase shift between two adjacent pulses, it is difficult to prepare dual reference pulses with the same phase relative to the LO. In this paper, we propose an improved method to get around this difficulty, which is demonstrated experimentally for a transmitter and a receiver connected by a 50 km single mode fiber. The phase noise measured in the experiment is 2.0×10−3rad2, which is comparable to the recent experimental results using heterodyne detection. This method simplifies the preparation of phase reference pulses and removes the obstacles for the application of homodyne detection in the LLO scheme. In addition, this method can also be used for the compensation of quadrature imbalance in heterodyne detection, then the performance of heterodyne detection can be improved.