We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude $\lambda$ 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 $\lambda$ 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.

• Received 21 May 2013

DOI:https://doi.org/10.1103/PhysRevA.88.052117