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

Abstract

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.

Extending the quantum tomography of a quasi-photon-number-resolving detector

“…In the quantum technology context, the relation between Bayesian probability and quantum probability has been discussed [34], and applications to quantum state tomography [35,36], parameter estimation [37,38], and learning quantum systems [39] have been demonstrated. In contrast to standard quantum tomography of a qPNRD, the Bayesian approach facilitates time-dependent POVM reconstruction [40], discrimination of different states of light [41,42], and assessment of the importance of the photon probability distribution before a photon is detected [43].…”