Quantum Fisher information is a key concept in the field of quantummetrology, which aims to enhance the parameter accuracy by using quantumresources. In this paper, utilizing a representation of quantum Fisherinformation for a general unitary parametrization process, we study unitaryparametrization processes governed by su(2) dynamics. We obtain the analyticalexpression for the Hermitian operator of the parametrization and the maximalquantum Fisher information. We find that the maximal quantum Fisher informationover the parameter space consists of two parts, one is quadratic in the timeand the other oscillates with the time. We apply our result to the estimationof a magnetic field and obtained the maximal quantum Fisher information. Wefurther discuss a driving field with a time-dependent Hamiltonian and find themaximal quantum Fisher information of the driving frequency attains optimumwhen it is in resonance with the atomic frequency.
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