  Quantum mechanics establishes the ultimate limit to the scaling of the
precision on any parameter, by iden- tifying optimal probe states and
measurements. While this paradigm is, at least in principle, adequate for the
metrology of quantum channels involving the estimation of phase and loss
parameters, we show that estimat- ing the loss parameters associated with a
quantum channel and a realistic quantum detector are fundamentally different.
While Fock states are provably optimal for the former, we identify a crossover
in the nature of the optimal probe state for estimating detector imperfections
as a function of the loss parameter. We provide explicit results for on-off and
homodyne detectors, the most widely used detectors in quantum photonics
technologies.
