title: Quantum metrology with unitary parametrization processes.
abstract: Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. Furthermore, H can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
authors.affiliation: Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China.
authors.forename: Jing
authors.initials: J
authors.lastname: Liu
authors.affiliation: Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China.
authors.forename: Xiao-Xing
authors.initials: XX
authors.lastname: Jing
authors.affiliation: 1] Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China [2] Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Xiaoguang
authors.initials: X
authors.lastname: Wang