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arXiv:2110.10484 · New Journal of Physics

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

Erik Fitzke, Robin Krebs, Thorsten Haase, Maximilian Mengler, G. Alber, Thomas Walther

Published Jan 28, 2022• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ac5004

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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.
Abstract Using numerical simulation methods that take into account the dead time effect, algorithms are developed to calculate the detector’s response for photon fluxes with different photon number distributions, including the Poisson, Fock, and thermal distributions. Based on the results obtained, a detector tomography method is developed, as well as an algorithm for identifying the corresponding elements of a positive operator-valued measure (POVM). Experimental studies using coherent states demonstrate close agreement between the calculation results and experimental data.
Using numerical simulation methods that take into account the dead time effect, algorithms are developed to calculate the detector’s response for photon fluxes with different photon number distributions, including the Poisson, Fock, and thermal distributions. Based on the results obtained, a detector tomography method is developed, as well as an algorithm for identifying the corresponding elements of a positive opera-tor-valued measure (POVM). Experimental studies using coherent states demonstrate close agreement between the calculation results and experimental data.
Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators.
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.
We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single-photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the average fidelity between the expected and reconstructed states is computed for qubits, qutrits, and entangled qubits.
Quantum optics is central to emerging quantum technologies such as quantum metrology and quantum information. The continuous variable (CV) approach to encoding information in a physical system, for example the electromagnetic field quadratures has significant advantages over discrete variables (DV) encoding. CV offers higher density encoding in a single optical state and on-demand state preparation for example. However, techniques for CV preparation, manipulation and measurement are not as well developed as the corresponding DV approach. In this thesis we present methods to characterize quantum detectors that operate in the CV regime, and discuss their application to CV state preparation. A quantum detector is described by its positive operator valued measure (POVM) set, with one operator for each measurement outcome. We present an experimental scheme for detector tomography, that is reconstruction of the POVM set of an unknown detector by means of measurement outcomes for a set of tomographically complete input states. We use this scheme to experimentally determine the POVM set of an avalanche photodiode (APD) and a time-multiplexed-detector (TMD) and compare the results to models of the detectors. We introduce a weak-homodyne photon-number-resolving detector (PNRD) , which uses a weak local oscillator beam to set a phase reference for the detection process. We develop a theoretical description of the sensitivity regimes for this detector using the Wigner phase space picture. We also present experimental detector tomography for a weak-homodyne detector based on two APDs. In many cases it is sufficient to calibrate the efficiencies of previously characterized PNRDs. We experimentally demonstrate a scheme using correlated photons produced by spontaneous parametric downconversion (SPDC) to determine the efficiencies of PNRDs, based on the photon number statistics of the source. The same SPDC source is also used to demonstrate preparation of photonic states in the photon number basis and for a first proof-of-principle experiment with a weak-homodyne PNRD based on a TMD.