  Quantum Fisher information is a central quantity in quantum metrology. We
discuss an alternative representation of quantum Fisher information for unitary
parametrization processes. The highlight of this representation is that 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. 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. Furthermore, 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 in the last.
