Protection Of Quantum Fisher Information In Open Quantum Systems

Quantum metrology is a discipline about quantum measurement and quantum statistical inference.It studies how to measure physical quantities accurately.After the development of quantum metrology,the classic Fisher information was extended to the quantum field.Quantum Fisher information as the highest theoretical precision of parameter estimation in quantum systems has been extensively studied.In this paper,we use the quantum Fisher information as the main indicator to study the problem of parameter estimation.The structure of this paper is as follows.In the first chapter,we introduce the knowledge about quantum metrology and open quantum systems.We discuss the development of quantum metrology and its application prospects,and introduce the research methods of open quantum systems.In the second chapter,we introduc the concept of quantum Fisher information.First,we introduc the quantum Cram′er-Rao theorem.The theorem tells us that the upper bound of the precision of the parameter estimate is given by the inverse of the quantum Fisher information.Therefore,if we want to improve the precision of the parameter estimation,it is necessary to select a suitable particle detection state to make the value of the quantum Fisher information larger.Next,we present the most common method for calculating quantum Fisher information.In chapter three,we study the protection of quantum Fisher information in entangled two-level quantum systems via classical driving.We obtain the dynamics of two and three entangled two-level atomic systems and numerically simulate the evolution of quantum Fisher information.We find that the QFI of the phase parameters encoded in entangled atomic states can be protected effectively whenall the classical fields that drive the atoms reach suitable strength.However,if one of the driving fields vanishes or is very weak,then the protection is seriously restricted and even possibly becomes worse.We show that the resonant driving,that is,the frequency of classical field equals that of atomic transition,is the most effective.In chapter four,we study the protection of quantum Fisher information for multiple phases in open three-level quantum systems via classical driving.We study the protection of quantum Fisher information of two phases encoded in an open V-type three-level atom embedded in a zero-temperature bosonic reservoir and driven by a classical field.It is found that the QFI of both of the two phases can be protected effectively when the strength of the driving field is adequate.The protective effect increases with the reducing of the frequency detuning between the classical driving field and the atomic transition.Narrow width of the environmental spectrum is also beneficial for the protection of QFI of the phases.In chapter five,we study the evolution of quantum Fisher information in open three-level quantum systems.We obtain the exactly analytical solutions for the dynamics of the dissipative three-level V-type and Λ-type atomic systems in the vacuum Lorentzian environments.We also study the dynamical evolution of quantum Fisher information,and find that for V-type and Λ-type atomic,when the center frequency of the Lorentzian environment is located at the middle between the two transition frequencies,the decaying of the quantum Fisher information is the fastest.Deviating from this middle frequency to the two sides,the decaying becomes slower and slower.The last chapter is the conclusion and outlook.