Finite-size Analysis Of Continuous-variable Quantum Key Distribution

Quantum Key Distribution(QKD)is a key distribution method in which two communication parties use quantum states as carriers of information and transmit a quantum channel to negotiate a key between two communication parties.Using these keys to encrypt the classical information,we can realize the theoretic unconditional security.The security of QKD is guaranteed by the Heisenberg uncertainty principle and the quantum nonclonability theorem of quantum mechanics,which has the characteristics of physical security quantum key distribution technology has been widely concerned and rapid development.Since the birth of the first QKD protocol,after 30 years of development,QKD has made remarkable progress both in experimental technology and theoretical security analysis.The discrete-variable QKD protocol represented by BB84,and the continuous-variable quantum key distribution protocol represented by GG02 protocol are gradually proved its theoretical unconditional security.In recent years,the QKD system has also been put into practical use.In 2013,China launched the "Beijing-Shanghai Mainline" quantum secure communications backbone network with a total length of about 2000 km.It is estimated that a second quantum secure communications trunk line,WuHe Mainline,will be established in 2018.The continuous-variable quantum key distribution(CV-QKD)protocol uses the information of the normal components of the light field to encode the information,and adopts the balance homodyne detection or heterodyne detection to obtain the information.The detection device has high response frequency and high detection efficiency,potential for high-speed communications.CV-QKD system and has good compatibility with optical network,and it is conducive to the promotion of their applications.Therefore,the CV-QKD protocol has drawn more and more attention.Among them,the most representative Gaussian modulation coherent state protocol(GG02)is the mainstream protocol adopted by most QKD systems,and the security theory proves also more perfect.The coherent state CV-QKD protocol is theoretically proved to be unconditional and secure.However,the practical CV-QKD system is vulnerable to hacker attacks due to the imperfection of the detection device.Therefore,a continuous variable measurement device independent(CV-MDI)protocol has been proposed.Since the measurement part of the protocol is completely handed down to untrusted third parties,the security of the protocol does not depend on the security of the probe,Therefore,the protocol can naturally resist all hacker attacks on the detection.Because the theoretical security analysis of CV-QKD protocol is based on the assumption that asymptotic schemes for exchanging infinite number of signals between two communicating parties,the actual communication capability of the CV-QKD protocol is limited and the exchangeable key length is limited.Therefore,the practical implementation of continuous-variable measurement-device-independent quantum key distribution(CV-MDI QKD)should not ignore the impact of finite-size.To solve this problem,we study the impact of the finite-size effect on the CV-MDI QKD protocol,mainly considering the finite-size effect on the parameter estimation procedure.The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters.We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol.It is proved that when Charlie's position is close to Bob,the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario.Finally,we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol.The overall results indicate that the finite-size effect has a great influence on the secret key rate of the CV-MDI QKD protocol and should not be ignored.