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We report on the first realization of time-dependent quantum detectortomography for commercially available InGaAs avalanche photo detectors. For theconstruction of appropriate time-dependent POVMs from experimentally measureddata, we introduce a novel scheme to calculate the weight of the regularizationterm based on the amount of measured data. We compare our POVM-based resultswith the theoretical predictions of the previously developed model by Gouzienet al. In contrast to our measurement-based construction of a time-dependentPOVM for photon detectors, this previous investigation extends atime-independent POVM to a time-dependent one by including effects of detectortiming jitter and dead time on the basis of particular model assumptionsconcerning the inner physical mechanisms of a photon detector. Our experimentalresults demonstrate that this latter approach is not sufficient to completelydescribe the observable properties of our InGaAs avalanche photo detectors.Thus, constructing the time-dependent POVM of a detector by direct quantumtomographic measurements can reveal information about the detector's interiorthat may not easily be included in time-independent POVMs by a priori modelassumptions.

Time-dependent POVM reconstruction for single-photon avalanche photo diodes using adaptive regularization