  We report on the first realization of time-dependent quantum detector
tomography for commercially available InGaAs avalanche photo detectors. For the
construction of appropriate time-dependent POVMs from experimentally measured
data, we introduce a novel scheme to calculate the weight of the regularization
term based on the amount of measured data. We compare our POVM-based results
with the theoretical predictions of the previously developed model by Gouzien
et al. In contrast to our measurement-based construction of a time-dependent
POVM for photon detectors, this previous investigation extends a
time-independent POVM to a time-dependent one by including effects of detector
timing jitter and dead time on the basis of particular model assumptions
concerning the inner physical mechanisms of a photon detector. Our experimental
results demonstrate that this latter approach is not sufficient to completely
describe the observable properties of our InGaAs avalanche photo detectors.
Thus, constructing the time-dependent POVM of a detector by direct quantum
tomographic measurements can reveal information about the detector's interior
that may not easily be included in time-independent POVMs by a priori model
assumptions.
