The Fisher information for measurements on open quantum systems

The quantum Cramer-Rao bound relates estimation sensitivity in quantum precision measurements to the distinguishability of different quantum states. We show that the theoretical sensitivity limit to parameters that govern the dynamics of an open quantum system coupled to a fully quantized environment can be evaluated from the reduced system master equation. We provide the bound for a laser driven two-state atom, where photon counting and homodyne detection of the fluorescence signal yield different sensitivity to the atomic and field parameters, while none of them exceed our general sensitivity limit.