Quantum Fisher information for unitary parametrization processes governed by arbitrary Lie algebras

Quantum Fisher information (QFI) is a key concept of quantum metrology, which is widely used in quantum parameter estimation. We introduce a general approach to analytically get the QFI of pure states for unitary parametrization processes governed by arbitrary finite dimensional Lie algebras. We show the universality of this approach by comparing the result of su (2) algebra with the previous work and applying it to su (1, 1) and su (3) algebras. For su (1, 1) case, there are some interesting findings. The phase of the initial coherent state has an optimal value for maximum QFI, and the QFI can vanish and revive during the time evolution.