Quantum parameter estimation affected by unitary disturbance

We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude λ associated to a unitary dynamics. By computing an analytical and general expression for the quantum Fisher information, we prove that the optimal estimation precision for λ cannot be outperformed through the addition of such a unitary disturbance. However, if the dynamics of the system is already affected by an external field, increasing its strength does not necessarily imply a loss in the optimal estimation precision.