Research On Postprocessing Algorithm For Continuous-variable Quantum Key Distribution At Extremely Low Signal-to-noise Ratio

Quantum key distribution(QKD)could generate unconditional secure keys.Its security is guaranteed by the basic principles of quantum physics.It can be obtained from the quantum non-cloning theorem and quantum uncer-tainty principle that if the illegal eavesdroppers perform any eavesdropping of quantum states in the process of QKD,they will disturb the quantum states and can be detected by the legitimate communication parities,thus the unconditional security of quantum keys are ensured.QKD protocols can be divided into discrete variables(DV)protocols and continuous variables(CV)protocols.For the single photon based DV protocols,the cost of system implementation is high in the aspect of single photon prepa-ration and measurement.For the Gauss modulation coherent states CV-QKD protocols,they can make use of the devices in classical optical communication,such as the lasers and the balance detectors.This greatly reduces the difficulty and the cost of quantum state preparation and quantum measurement.Thus,CV-QKD protocols attract lots of attention.In recent years,CV-QKD protocols have not only made ogreat breakthroughs in the theory,but also have made rapid development in the experiments.CV-QKD has developed rapidly,but compared to single photon protocols,its transmission distance is short,and its key generation speed is slow currently.Postprocessing is one of the key factors that restrict the above-mentioned perfor-mance of the system.To solve these problems,this paper makes a deep research on postprocessing.The main work of this paper is shown as follows:1.High reconciliation efficiency postprocessing algorithms.Reconcili-ation efficiency has an important impact on the transmission distance of the system.In this paper,two efficient postprocessing information reconciliation algorithms are proposed.One is slice reconciliation based on polar codes.Slice reconciliation is studied first,including quantization of continuous variables,mutual information calculation at each level etc.and then multi-level encoding and decoding algorithm is realized based on polar codes.The reconciliation efficiency can be obtained to over 92%.The other is multidimensional rec-onciliation based on MET-LDPC codes.Multidimensional reconciliation is studied first.Then the degree distribution is designed by density evolution algorithm of MET-LDPC codes.The parity check matrices are constructed according to its degree distribution whose error correction performance is close to Shannon limit.By combining these two algorithms,an efficient information reconciliation algorithm is realized at extremely low signal-to-noise ratios,and the reconciliation efficiency is achieved to 98.66%which supports over 200km of CV-QKD systems.2.High performance postprocessing algorithm for practical application.Aiming at the problem of low data utilization in practical systems,a high data utilization postprocessing algorithm is proposed,which can use the whole raw data for both parameter estimation and key extraction.This method improves the precision of parameter estimation and the accuracy of secret key rate.The results show that the secret key rate and transmission distance are obviously improved.Aiming at the problem of quantum channel fluctuation in practical systems,a rate-adaptive reconciliation al gorithm is proposed,which can flexibly and equivalently adjust the error correction code rate according to the signal-to-noise ratio of the practical quantum channel.This method can obtain high reconciliation efficiency within a certain range of signal-to-noise ratios.An arbitrary length privacy amplification algorithm is proposed,which reduces the implementation complexity and guarantees the security of the practical system under finite-size effect.3.Research and implementation of high-speed real-time postprocessing algorithm.Several methods are proposed to improve the implementation speed of error correction step,including simplifying iterative decoding algorithm of MET-LDPC codes,improving the storage structure of parity check matrices,and performing error correction of multi-codewords in parallel on GPU,which achieves the decoding speed of 30.39 Mbps.A high-speed privacy amplification algorithm is proposed with arbitrary length.Fast Fourier transform is used to reduce the complexity of the algorithm,and the speed of privacy amplification is achieved to 1.35Gbps based on GPU.After each step of postprocessing obtains high speed implementation,all the steps are performed in parallel based on multi-threading technology.The overall speed of postprocessing reaches 16.37M pulses per second,which improves the real-time key generation rate.4.A complete postprocessing program is designed and developed accord-ing to the high performance algorithms mentioned above by considering the characteristics of the practical system.In addition to the implementation of the postprocessing functions,the program also includes two-terminal commu-nication,the overall control system,as well as the operation status monitoring.Several user graphical interfaces are designed to display the parallel workflow of postprocessing and the process of secure communication using quantum keys.The postprocessing program has been applied for practical systems,such as the field tests in Xi'an.Guangzhou and Qingdao,which have realized high-speed real-time key generation and creat a new commercial optical fiber transmission record.