Research On Reconciliation For Continuous Variable Quantum Key Distribution

Communication technology is playing an increasingly important role in today's society.The public is paying more attention to whether the security of communication can be guaranteed.Quantum key distribution enables the sender and receiver to still share the key in the presence of an eavesdropper and has proven to be absolutely secure.Reconciliation is a stage of quantum key distribution.Reconciliation is used for error correction.Under the current research,the optimization of reconciliation mainly focuses on two aspects:the application of better error-correcting codes and the improvement of decoding algorithm.Low-Density Parity-Check(LDPC)Codes are very suitable for quantum key distribution systems.This paper is devoted to the research of key agreement algorithm.By studying reconciliation algorithm,this paper adopts multidimensional reconciliation with better performance and improves the decoding algorithm.The simulation results show that the improved algorithm has better performance.The main contents of this paper are as followsThis paper studies the multidimensional reconciliation process of continuous variable quantum key distribution,and finds that the noise of its virtual channel obeys t-distribution.For multidimensional reconciliation with dimension d,the SNR of its virtual channel is not equal to that of the quantum channel,but has a(d-2)/d proportional relationship.For this relationship,when multidimensional reconciliation is applied,the modulation variance of the channel can be adjusted to(d-2)/d the original modulation variance to balance the security problem caused by the SNR mismatch.In this paper,we use MATLAB to simulate and calculate the SNR of virtual channel and quantum channel.The simulation results show that there is an(d-2)/d ratio relationship between the SNR of virtual channel and the SNR of quantum channelIn this paper,a multidimensional reconciliation based on QC-LDPC(Quasi-Cyclic LDPC)codes is constructed.First,the original key is converted into d-dimensional vector,and then each vector is normalized,maximized distance and rotated using rotation matrix.In the decoding process,a belief propagation Algorithm(BP algorithm)is used.The QC-LDPC codes with bit rates of 0.5,0.667,0.75 and 0.83 are used for error correction comparison.It is found that the smaller the bit rate,the better the performance of error correction.The QC-LDPC codes with bit rates of 0.5 and code lengths of 576,1152 and 2304 are used for simulation and comparison,and the longer the code length,the better the performance of error correction.This paper improves the decoding process of multidimensional reconciliation.Considering that the noise of multidimensional reconciliation virtual channel obeys t-distribution,which is contrary to the original BP decoding assumption that the channel noise obeys Gauss distribution,the BP algorithm is improved.Through simulation,the bit error rate(BER)and frame error rate(FER)of the multidimensional reconciliation scheme using the original BP decoding algorithm and the improved BP decoding algorithm are calculated respectively.The simulation results show that the error rate and frame rate of the improved BP decoding algorithm are much lower than those of the original BP decoding algorithm.Especially for high SNR channels with SNR greater than 2,the improved BP decoding algorithm can completely remove the channel noise.Therefore,multidimensional reconciliation based on QC-LDPC codes using improved BP decoding algorithm can be more suitable for continuous variable quantum key distribution with low SNR,and can better achieve long-distance continuous variable quantum key distribution.