Maximal quantum Fisher information for general su(2) parametrization processes

Abstract

Quantum Fisher information is a key concept in the field of quantum\nmetrology, which aims to enhance the parameter accuracy by using quantum\nresources. In this paper, utilizing a representation of quantum Fisher\ninformation for a general unitary parametrization process, we study unitary\nparametrization processes governed by su(2) dynamics. We obtain the analytical\nexpression for the Hermitian operator of the parametrization and the maximal\nquantum Fisher information. We find that the maximal quantum Fisher information\nover the parameter space consists of two parts, one is quadratic in the time\nand the other oscillates with the time. We apply our result to the estimation\nof a magnetic field and obtained the maximal quantum Fisher information. We\nfurther discuss a driving field with a time-dependent Hamiltonian and find the\nmaximal quantum Fisher information of the driving frequency attains optimum\nwhen it is in resonance with the atomic frequency.\n