Research On Parameters Estimation And The Non-markovianity Of Quantum Channel

With the rapid development of informationization,almost all applications are inseparable from the interaction of information.In the process of information exchange,the most important thing is to ensure the security of information transmission.In traditional cryptography,usually information security is guaranteed by computational complexity theory.However,the rapid development of quantum computers poses a great threat to traditional information encryption methods.Compared with the traditional secure communication,the quantum cryptography communication based on Quantum Key Distribution(QKD)has attracted more and more researchers’ attention because of its unconditional security.In the practical QKD systems,since quantum states are affected by noise and other factors in the transmission process,the key rate of the QKD systems is not very efficient,in order to improve the key rate,it is of great significance to study the transmission characteristics of the quantum states in the quantum channels.According to this,we mainly focuse on the quantum channel parameter estimation and its nonMarkovianity.Firstly,we introduce the development status at home and abroad of quantum cryptography communication and the research status of quantum channel parameter estimation.Then the related physics foundation of the quantum cryptography communication are presented,which mainly include five postulates of quantum mechanics,Heisenberg’s uncertainty principle and the no-cloning theorem.Two typical quantum key distribution protocols,several typical quantum channels,and open quantum systems are introduced in briefly.Secondly,taking the Pauli channel as an example,we research the parameter estimation of quantum channels.The maximum likelihood estimation method is applied to the parameter estimation of the quantum Pauli channel,and in case of the extended channel,we investigate the quantum Fisher information(QFI)when the input of the channel are entangled states.Analysis results show that when the input state is the maximally entangled state,the parameter estimation system has the maximum quantum Fisher information and the parameter estimation accuracy is the highest.In practical applications,quantum states may suffer from the loss of particles under the effect of the channels.Therefore,we analyze the effect of single-particle loss on the quantum Fisher information and compare it with the case of no particle loss.The results show that when the particle loss occurs in the transmission process,the accuracy of the parameter estimation will be reduced significantly.Thirdly,based on the non-Markovian depolarization channel,the property of the nonMarkovianity of quantum channels is researched.We first analyze the fidelity of polarization states travelling through a non-Markovian optical fiber depolarizing quantum channel.The analysis results verify the non-Markovianity of the system.At the same time,the quantum bit error rate(QBER)of a polarization coded BB84 quantum key distribution system under non-Markovian depolarizing channel is also discussed.Analysis results show that when the coupling strength between the system and the environment is large,the QBER oscillates.There are several security regions in which QBER is smaller than the security threshold in such a non-Markovian channel.These will provide references for designing polarization compensation scheme and estimating secure distances.Finally,we summarize the paper and give some suggestions for the further research.