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.
Advances in photonics require photon-number resolved simulations of quantum optical experiments with Gaussian states. We demonstrate a simple and versatile method to simulate the photon statistics of general multimode Gaussian states. The derived generating functions enable simulations of the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics of Gaussian states as well as of multimode photon-added and photon-subtracted Gaussian states. Numerical results are obtained by automatic differentiation of these generating functions by employing the machine learning framework PyTorch. Our approach is particularly well suited for practical simulations of the photon statistics of quantum optical experiments in realistic scenarios with low photon numbers, in which various sources of imperfections have to be taken into account. As an example, we calculate the detection probabilities for a recent multipartite time-bin coding quantum key distribution setup and compare them with the corresponding experimental values.
In our laboratory, we employ two biphoton sources for quantum key distribution. The first is based on cw parametric down-conversion of photons at 404 nm in PPKTP waveguide chips, while the second is based on the pulsed parametric down-conversion of 775 nm photons in PPLN waveguides. The spectral characterization is important for the determination of certain side-channel attacks. A Hong-Ou-Mandel experiment employing the first photon source revealed a complex structure of the common Hong-Ou-Mandel dip. By measuring the spectra of the single photons at 808 nm, we were able to associate these structures to the superposition of different transverse modes of the pump photons in our waveguide chips. The pulsed source was characterized by means of single-photon spectra measured by a sensitive spectrum analyzer as well as dispersion-based measurements. Finally, we also describe Hong-Ou-Mandel experiments using the photons from the second source.
Simultaneous pairwise quantum key distribution between four parties was demonstrated by implementing an entanglement-based phase-time coding protocol with a type-0 SPDC photon source. The star-shaped network is scalable to dozens of users.
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