Influence Of Prior Distribution Of Frequency On Effect Of Two Noises In Bayesian Frequency Estimation

Accurate inference of physical parameters in physical system is an important part of theoretical research and experimental research.Quantum parameter estimation is to study how to use small quantum system to infer statistically physical parameters.Therefore it is very important both for theoretical research and experimental research.All real quantum systems are affected inevitably by the external environment,the presence of noise will affect the accuracy of parameter estimation.So it is necessary to study the mechanism of noise on the parameter estimation process.In general,we would have prior information of the parameter.How to use these information to improve the estimation precision is a very interesting topic.In this thesis,we estimate the intensity of magnetic filed by adopting a 1/2 spin system which is influenced by the noise.First,we assume that system is in an optimal initial state,then let it interact with a magnetic field and noise.Finally,we can infer the intensity of the magnetic field by measuring the system.Given the general Hamiltonian of the system,we obtain the Bloch vector,and then we draw a Bayesian cost expression under random telegraph noise and colored noise.Finally,we study the effects of three prior frequency distribution on the two kinds of noise in Bayesian frequency estimation.We find that for the broad prior frequency distribution case,the influence of non-Gaussianity on the estimation is very small.While for the narrow prior frequency distribution case,the influence of non-Gaussianity on the estimation is strong.Therefore,if we have known a prior probability distribution in the experiment,we can effectively improve the accuracy of measurement using the non-Gaussianity of the noise.