Research Of Decoy-state Method And Post-processing Process In Quantum Key Distribution

Quantum key distribution can provide unconditional secure shared keys for both parties(Alice and Bob)in long-distance communications.The unconditional security of keys is guaranteed by the laws of quantum mechanics.The ideal quantum key distribution protocols require perfect single photon sources.At present,due to the limitation of technology,people always adopt weak coherent state sources to replace perfect single photon sources.Due to the existence of multi-photon pulses of a weak coherent state source,the eavesdropper(Eve)may launch the photon number splitting attack,which greatly reduces the secure key rate and even makes it impossible to extract the secure key completely.Fortunately,the decoy-state method proposed later can resist this attack very well.Quantum key distribution includes the quantum signal transmission process and post-processing process.The former mainly includes the preparation,transmission,reception，and measurement of quantum states.The latter mainly includes error rate estimation,error correction and privacy amplification,and other processes.In particular,with the rapid development of practical quantum key distribution systems,post-processing,especially error correction and privacy amplification,has become a bottleneck restricting the development of quantum key distribution technology.This paper mainly studies four key problems of the decoy-state method and the post-processing process in quantum key distribution.Among them,the decoy-state method part mainly includes the verification problem of the assumption that signal state and decoy state are indistinguishable,the existing decoy-state method does not care about the existence of photon number splitting attack and only adopts the single photon component coding problem,and the problem of loose boundary values when estimating statistical fluctuations by the existing analysis method of the central limit theorem.The solution to these three problems will respectively realize the security verification of the decoy-state method,the enhancement of the theoretical secure key rate,and the enhancement of the actual secure key rate of the decoy-state method.The postprocessing part mainly considers the relative independence of error correction and privacy amplification and explores the possibility of time-division multiplexing for error correction and privacy amplification.The solution to this problem will greatly reduce the calculation and storage cost of post-processing.On the whole,there is a progressive relationship among the four research contents,and the solution of the above problems will further promote the engineering and practical application of quantum key distribution,and broaden the application range of quantum key distribution.Specific research contents are as follows:(1)In order to verify the assumption that signal and decoy state are indistinguishable in the decoy-state method,we use the difference of photon number probability distribution caused by different intensities of signal and decoy state,combined with Bayesian decision to verify the rationality of the assumption.Moreover,the security of the assumption is verified by comparing the secure key rates before and after the photon number splitting attack.In summary,the security analysis of decoy-state method is improved from the above two aspects.(2)In order to solve the problem that the existing decoy-state methods do not care about the existence of photon number splitting attacks and only use single photon component coding,we introduce the statistical hypothesis testing method into decoy-state protocols.Within the allowed range of error probability,when the judgment result is that there is no basic type of photon number splitting attack on the channel,both single photon and multi-photon pulses with the same base and a response or a successful Bell state measurement event are used to generate the key,which improves the theoretical secure key rate compared with the existing decoy-state method.(3)To solve the problem of loose boundary value when statistical fluctuation is considered by the existing method of the central limit theorem,we combine the method of the central limit theorem and the normal approximation theorem,reduce the number of boundaries required,and the estimation deviation,and improve the estimation accuracy.Finally,we give the lower bound of the tight actual secure key rate of decoy-state BB84 protocol when considering statistical fluctuation.In particular,when the number of pulses sent is small(e.g.,107),the advantages of our approach are more obvious.(4)In view of the relative independence of error correction and privacy amplification in the existing post-processing process,based on the principle of correspondence between error correction code and hash function family,we proposed the idea of combining error correction and privacy amplification with time-division multiplexing and tested them respectively from the perspectives of error correction and privacy amplification.Although the existing error correction algorithm commonly used in quantum key distribution and its corresponding hash function family or the common privacy amplification method and its corresponding error correction code cannot realize time-division multiplexing of error correction and privacy amplification temporarily,according to the principle of correspondence between error correction code and hash function family,the idea of time-division multiplexing for error correction and privacy amplification is possible.In addition,the research on time-division multiplexing for error correction and privacy amplification has some practical significance.Once the idea of time-division multiplexing for error correction and privacy amplification is realized,it will further reduce the calculation and storage cost of the post-processing process,reduce the deployment cost of quantum key distribution,and help promote the practical engineering of quantum key distribution.