The bounds of Fisher information induced by the superposed input states

Quantum Fisher information as an important quantity in quantum metrology determines the upper bound of the measurement accuracy. It is shown that the quantum feature such as entanglement can improve quantum Fisher information in some cases. Here we study how quantum coherence affects the quantum Fisher information from a general point of view. We find out that the bounds induced by the superposed states can well restrict the quantum Fisher information in a general parameter estimation scheme. As applications, we demonstrate these bounds by a parameter estimation process with the superposition input state undergoing different quantum channels.