Geometric Representation Of Quantum Fisher Information And Precise Measurement Of Rotation

With the development of the information technology,quantum information,as an interdisciplinary subject of quantum mechanics and informatics,has attracted more and more attention.The Fisher information plays an important role in the parameter estimation of physical systems.There are two main research problems in this paper,the representation of the quantum Fisher information under the Majorana's stellar representation and the measurement of rotation accuracy in the multi-atom Sagnac interferometer.In Chapter 1,the background and current status of our researches will be briefly introduced.In Chapter 2,we will give brief introductions on the classical Fisher information,the quantum Fisher information,and the quantum Fisher information matrix.In addition,how to calculate the quantum Fisher information in the case of non-normalized state and unitary parameterization process will be discussed separately.In Chapter 3,we will discuss the quantum Fisher information under the Majorana's stellar representation.In other words,we will use the relationship of the Bloch vector of each Majorana star and the partial derivative of the estimated parameter to represent the quantum Fisher information.First,we will show that the spin-J state can be expressed by 2J Majorana stars on the Bloch sphere under the Majorana's stellar representation.Next,we will introduce the relationship of these Bloch vectors,and the relationship of the two-level pure states of these Bloch vectors.Finally,we will take J=1/2,J=1,and J=3/2 as examples to show the calculation processes and give specific calculation methods and simplification techniquesIn Chapter 4,we will use the multi-atom Sagnac interferometer as the research model to show the optimal measurement direction and the corresponding maximum classical Fish-er information under the classical Parity measurement.First,we will introduce the model.We will give a general initial state to calculate the quantum Fisher information.Secondly,we will use the general initial state and an arbitrary direction Parity measurement operator to calculate the optimal measurement direction and the corresponding maximum classi-cal Fisher information.Finally,we will take the partially entangled state and the global entangled state as examples to analyze the above results.In Chapter 5,we have a summary of the full text.