Study On Quantum Parameter Estimation In Open Quantum Systems

Quantum parameter estimation is a discipline related to measurement of physical quantity and statistical inference in quantum systems.It is widely used in quantum gyroscope,quantum frequency standards,gravitational-wave observatory,atomic clock,quantum imaging,and quantum radar.How to use quantum resources to improve the estimation accuracy of system parameters is the core subject of quantum parameter estimation.Based on the open quantum systems,this thesis focuses on the improvement and numerical calculation of the accuracy of quantum parameter estimation.Chapter 1 reviews the development of quantum parameter estimation.At the same time,we introduce the limitation of parameter estimation and the representation of the estimation accuracy.Chapter 2 mainly introduces the mathematical foundations of studying quantum parameter estimation.Taking the Fisher information and Cramér-Rao inequality as the core,we introduce the definitions of classical and quantum parameter estimation accuracies and the relationship between these two accuracies.The Lindblad equation and the stochastic master equation,which are used to describe dynamic evolutions of open quantum systems,are also introduced.In addition,some useful knowledge of mathematics required in our research are also briefly introduced,including multi-dimensional It? formula,the Metropolis Hastings algorithm,and the Makov Chain Monte Carlo integration.In chapter 3,we investigate quantum parameter estimation based on linear and Kerr-type nonlinear Hamiltonian controls over a lossy bosonic channel with considering the dissipation rate as an unknown parameter.It shows that while the accuracy of parameter estimation is improved,the state of the system incurs a significant deformation.Therefore,we propose a multi-objective model to optimize the two conflicting objectives:1)maximizing the Fisher information to improve the parameter estimation accuracy;2)minimizing the deformation of the system state to maintain the fidelity.Finally,simulations of a simplified ?-constrained model demonstrate the feasibility of the Hamiltonian control in improving the accuracy of the quantum parameter estimation.Chapter 4 focuses on the quantum parameter estimation in circuit quantum electrodynamics via continuous weak measurement.To reduce the complexity of computation,we first prove that any quantum stochastic master equation for un-normalized states can correspond to the evolutions of some normalized states.In the latter case,the Fisher information can be given by the form of log-likehood functions.Then according to the Metropolis Hastings algorithm and the Markov Chain Monte Carlo integration,we propose a new algorithm to numerically calculate the Fisher information.The feasibility and effectiveness of the proposed algorithm are confirmed through some simulation results.Based on the proposed algorithm,the effects of the measurement operator and the measurement efficiency on the Fisher information are preliminarily discussed,respectively.Chapter 5 denotes the conclusion and prospect.