Research On Post-processing In Quantum Key Distribution

Quantum key distribution(QKD)allows two authorized parties(Alice and Bob)obtain consistent and secure key with the principles of quantum mechanics.QKD is divided into quantum information processing stage and classical information processing stage.In quantum information processing stage,Raw key is generated by quantum signal generation,transmission and detection in quantum channel.In classical information processing stage(QKD post-processing stage),secure key is purified by basis sifting,parameter estimation,quantization,error correction,privacy amplification and authentication in classical channel.In discrete-variable QKD,parameter estimation is to estimate error rate of sifted key,key reconciliation is error correction.In continuous-variable QKD,parameter estimation is to estimate channel noise and transmittance,key reconciliation includes quantization step and error correction step.This paper is on research parameter estimation and key reconciliation of QKD post-processing stage.The main contributions are as follows:1.The method to compute optimal sampling rate is proposed when estimating error rate with random sampling method.For discrete-variable QKD,we present the connection between sampling rate and erroneous judgment probability,depict the relationship between sampling rate and secure key generation rate,propose a method to compute optimal sampling rate.Let weighted average of secure key generation rates be the measure of optimal sampling rate.Optimal sampling rate can make final secure key generation rate reach its maximum with high probability.These results can be applied to choose the optimal sampling rate and improve the performance of QKD system with finite resources.2,For discrete-variable QKD,by combining parameter estimation with error correction,adaptive error rate estimation method is proposed.First,sifted key is divided into several blocks averagely,the error rate of the first block sifted key is obtained by contrast 20% of the first block sifted key.Let the error rate of the i(i ?1)block sifted key be the estimated value of error rate of the i(10)1 block sifted key.Then,the i(10)1 block sifted key is corrected,error rate of the i(10)1 block sifted key is obtained.According to this method,the rest blocks can proceed error rate estimation and error correction respectively.If error correction is failed for a block,this block sifted key is discarded,contrast 20% of the next block sifted key and repeat the above process.The new error rate estimation method saves the time of error rate estimation,greatly reduce the loss of the key in QKD system.3,For Cascade protocol and LDPC codes,the upper bounds of leaked information in error correction are given,the method to eliminate leaked information is proposed.For Cascade protocol,the upper bound of leaked information is the number of comparison bits.the method to eliminate leaked information is tracking each circle.Record the leaked information in each circle,and all the leaked information will be eliminated after error correction.For LDPC codes,the upper bound of leaked information is the length of syndrome.Some sifted key corresponds to the linearly independent columns of check matrix,discarding these sifted key is equal to eliminating the leaked information.The research results can provide theoretical basis and technical guidances for the design and implementation of error correction.4,Spherical reconciliation is proposed for a continuous-variable QKD protocol.The efficiency and complexity of key reconciliation method are significant for the performance of continuous-variable QKD systems.Spherical reconciliation is based on spherical quantization and non-binary LDPC codes.In spherical reconciliation,firstly Alice or Bob's symbols are transformed to the points in the unit sphere completely.Then the points on the unit sphere are quantified to discrete variables with quantization function.Later parts of bits of discrete variables are discarded to reduce bit error rate.Finally,non-binary LDPC codes are used to decode remaining discrete variables and symbols,Alice and Bob obtain consistent and secure binary keys.Compared with slice reconciliation,spherical reconciliation can extend the transmission distance from 41 km to 56 km.Compared with multidimensional reconciliation,spherical reconciliation can extend the transmission distance from 60 km to 78 km.