Standard Deviation And Fisher Information Of Superpostion States

The state superposition principle directly leading to the coherence of a quantum state is one of the fundamental features in quantum mechanics.Almost all the other quantum features such as quantum entanglement,quantum correlation quantum non-locality and so on are closely related to the superposition principle.With the development of quantum information theory and experiment,the quantum mechanical features have become the useful physical resources in quantum information processing tasks.So,the research on the quantum fundamental features is not only an important research subject,but also a key task in the relevant researches in the field of quantum information.In this thesis,we mainly study the influence of the state superposition principle on the standard deviation and the Fisher information during the quantum measurement process.The thesis includes four chapter and the 3rd and 4th chapters are the main jobs done during the period of master degree study.In Chap.1,the development of the quantum informatics and quantum metrology as well as the outline of this thesis are briefly introduced.In Chap.2,we detailly introduce the fundamental knowledge on the quantum metrology,the standard deviation and the quantum uncertainty which is closely related to the standard deviation;Especially,the state superposition principle and the development of its research on the entanglement of superposed states are reviewed.In Chap.3,we study the distribution of the standard deviation among the different components of a superposition state.It is found that standard deviation of an observable on a superposition state can be well bounded by the standard deviations of the superposed states.We also show that the bounds also serve as good bounds on coherence of a superposition state.As a further generalization,we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.In Chap.4,we study how quantum coherence affects the quantum Fisher information from a general point of view.We find out that the bounds induced by the superposed states can well restrict the quantum Fisher information in a general parameter estimation scheme.As applications,we demonstrate these bounds by a parameter estimation process with the superposed input state undergoing different quantum channels.Finally,we give the summary of this thesis.