Quantum Estimation In Interferometers

A typical measurement model consists of three parts:input source,parameter introduction scheme,output.Quantum measurement refers to the consideration of quantum effects in the input source and measurement scheme to improve the measurement accuracy of the parameters.Compared to classical measurements that do not take quantum effects into account,quantum measurements can improve measurement accuracy from the scattered noise limit to the Heisenberg limit.To design a parameter introduction scheme,the choice of measuring instrument is particularly important.In this paper,the performance of two relatively common measurement instruments in quantum measurement is investigated.In the first two chapters of this paper we introduced the research background and briefly reviewed the history of quantum measurement.We then introduced the theoretical basis of measurement.We reviewed the Cramer-Rao inequality and the corresponding Fisher information that scale the uncertainty of the parameter to be measured.We then extend these results to the quantum case,introducing the quantum Cramer-Rao inequalities and the corresponding quantum Fisher information.We then further extend these results to the multiparameter case,introducting the multiparameter quantum Cramer-Rao inequality and the corresponding multiparameter quantum Fisher information matrix.In Chapter three we discuss the application of the Mach-Zehnder interferometer in quantum measurements.We first operatorize the interferometer,and then we calculate the quantum Fisher information for the general input state,the specific input state,and analyze the conditions that need to be satisfied for the input state phase to maximize the Fisher information,such conditions are called phase matching conditions.We also compute the quantum Fisher information for the Mach-Zehnder interferometer with loss case and examine the corresponding phase matching conditions.On this basis we discuss the optimization of quantum Fisher information for both consistent and inconsistent loss rates of the two arms of the interferometer.In Chapter four we discuss the application of the matter-wave Sagnac interfer-ometer in two-parameter quantum measurements.We choose as the input state the maximum entangled state produced by a group of atoms with intrinsically endowed angular momentum bounded by a harmonic potential well.By means of a reference system transformation we obtain the state-dependent Hamiltonian of the rotating Sagnac interferometer,and hence the evolution operator.With the evolution operator we compute the quantum Fisher information matrix for the two parameters to be measured,and then use the multiparameter Cramer-Rao inequality to obtain the lower bounds on the variances of the two parameters.We analyze how optimization can be used to improve the measurement precision and give expressions for optimal measurement results.In Chapter five we have a summary of the full text.