Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2403.11673 · Physical Review A

Experimental retrieval of photon statistics from click detection

Suchitra Krishnaswamy, F. Schlue, Laura Ares, Vladyslav Dyachuk, Michael Stefszky, Benjamin Brecht, Christine Silberhorn, Jan Sperling

Published Aug 16, 2024• 8 citations
arXivHTMLPDF

Abstract

We utilize click-counting theory for the reconstruction of photon statistics, employing an analytic pseudoinversion method. A reconfigurable time-bin multiplexing, click-counting detector is experimentally implemented, allowing for altering the photon-number resolution. A detector tomography is carried out, yielding vital measurement features, such as quantum efficiencies and cross-talk rates. We gauge the success of the pseudoinversion by applying the Mandel and binomial parameters, resulting in an additional interpretation of these parameters for the discrimination of distinct quantum statistics. For coherent states, which lie at the classical-nonclassical boundary, both parameters are highly sensitive measures, probing the kind of statistics and the reconstruction performance. In addition, we apply a loss deconvolution technique to account for detection losses.

DOI
10.1103/physreva.110.023717

Related papers

Direct calibration of click-counting detectors

Martin Bohmann, Regina Kruse, Jan Sperling +2 more

We introduce and experimentally implement a method for the detector calibration of photon-number-resolving time-bin multiplexing layouts based on the measured click statistics of superconducting nanowire detectors. In particular, the quantum efficiencies, the dark count rates, and the positive operator-valued measures of these measurement schemes are directly obtained with high accuracy. The method is based on the moments of the click-counting statistics for coherent states with different coherent amplitudes. The strength of our analysis is that we can directly conclude---on a quantitative basis---that the detection strategy under study is well described by a linear response function for the light-matter interaction and that it is sensitive to the polarization of the incident light field. Moreover, our method is further extended to a two-mode detection scenario. Finally, we present possible applications for such well-characterized detectors, such as sensing of atmospheric loss channels and phase sensitive measurements.

arXiv:1611.04779•Physical Review A•Mar 8, 2017•24 citations

Uncovering Quantum Correlations with Time-Multiplexed Click Detection

Jan Sperling, Martin Bohmann, W. Vogel +4 more

We report on the implementation of a time-multiplexed click detection scheme to probe quantum correlations between different spatial optical modes. We demonstrate that such measurement setups can uncover nonclassical correlations in multimode light fields even if the single mode reductions are purely classical. The nonclassical character of correlated photon pairs, generated by a parametric down-conversion, is immediately measurable employing the theory of click counting instead of low-intensity approximations with photoelectric detection models. The analysis is based on second- and higher-order moments, which are directly retrieved from the measured click statistics, for relatively high mean photon numbers. No data postprocessing is required to demonstrate the effects of interest with high significance, despite low efficiencies and experimental imperfections. Our approach shows that such novel detection schemes are a reliable and robust way to characterize quantum-correlated light fields for practical applications in quantum communications.

arXiv:1503.08028•Physical Review Letters•Jul 7, 2015•59 citations

PNR detector tomography using an analytical unequal-channel model and a hybrid reconstruction approach

G. V. Avosopiants, Konstantin G. Katamadze, N. A. Borshchevskaya +4 more

Abstract Though photon-number-resolving (PNR) detectors based on multiplexed threshold elements are key tools for quantum optics and quantum information, yet accurate calibration of their response in the presence of imperfections remains challenging. Here we develop a model for a four-channel PNR detector designed as a superconducting nanowire single-photon detector (SNSPD) array, allowing for unequal channel transmission coefficients and dark counts. Closed-form expressions for the click probabilities and transfer-matrix elements are obtained for coherent-state probes, and a numerical study quantifies the range of channel imbalance where the commonly used equal-channel, single-parameter approximation fails. Applying this framework to experimental data from a four-channel PNR SNSPD, we show that direct model-based fits do not reproduce the measured click statistics probably because of inter-channel cross-talks. To overcome this, we implement a hybrid quantum detector tomography scheme that combines a model-based fit to the mean click number with a data-driven reconstruction of the low-photon subspace. The resulting transfer matrix reproduces the experimental click statistics with average fidelity above 99.9% and provides a robust description of the detector in the presence of cross-talks and other non-idealities.

Laser Physics Letters•Dec 1, 2025•0 citations

Direct estimation of $g^{(2)}(0)$ from click statistics of a multiplexed detector

Jaromír Fiurášek

We present and theoretically analyze a method for direct estimation of the second-order correlation function $g^{(2)}(0)$ from the click statistics of a multiplexed detector composed of M binary on-off detection channels. The method uses linear estimators of the first and second moments of the photon-number operator and can provide accurate results even for optical fields with substantial mean photon numbers. For a fixed number of channels, the detection range can be extended by introducing additional losses before the detector. We demonstrate the performance of the method for coherent, thermal, amplitude-squeezed, and photon-added coherent states. We also derive a nonclassicality criterion based on the estimated correlation function and show how the method can be adapted to unbalanced detectors. Our work establishes direct estimation of $g^{(2)}(0)$ as a simple and versatile method for quantitatively characterizing quantum light using multiplexed click detectors.

quant-pharXiv:2610.03040•Oct 5, 2026•0 citations

Quantum state engineering by click counting

Jan Sperling, W. Vogel, G. S. Agarwal

We derive an analytical description for quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation using correlated light fields, photon addition, and photon subtraction processes. Using a postselection procedure to a particular number of clicks of the detector system, the output states reveal a variety of quantum features. The rigorous description allows the identification and characterization of fundamentally unavoidable attenuations within given processes. We also generalize a known scenario of noiseless amplification with click detectors for the purpose of the preparation of various types of nonclassical states of light. Our exact results are useful for a choice of experimental parameters to realize a target state.

arXiv:1403.1044•Physical Review A•Apr 17, 2014•63 citations

Measurement of photon number statistics using photon-number resolving detectors

Nicola N Low, Sai Sreesh Venuturumilli, Michal Bajcsy

We investigate the use of a photon-number resolving (PNR) detector as an alternative method for measuring the second-order correlation function g2(0). Our implementation employs four spatially multiplexed single-photon detectors to reconstruct the photon number distribution P(n) from click statistics. We estimate g2(0) for both coherent and quantum dot excition emission, and compare the results to those obtained from a conventional Hanbury Brown-Twiss (HBT) setup. In the single-mode regime, we observe close agreement between both approaches. We additionally compare the acquisition times required for each method and find that PNR-based measurements enable faster estimation of g2(0), offering potential advantages for scalable characterisation of quantum light sources.

Photonics for Quantum (PfQ)•Jul 18, 2025•0 citations
We utilize click-counting theory for the reconstruction of photon statistics, employing an analytic pseudoinversion method. A reconfigurable time-bin multiplexing, click-counting detector is experimentally implemented, allowing for altering the photon-number resolution. A detector tomography is carried out, yielding vital measurement features, such as quantum efficiencies and cross-talk rates. We gauge the success of the pseudoinversion by applying the Mandel and binomial parameters, resulting in an additional interpretation of these parameters for the discrimination of distinct quantum statistics. For coherent states, which lie at the classical-nonclassical boundary, both parameters are highly sensitive measures, probing the kind of statistics and the reconstruction performance. In addition, we apply a loss deconvolution technique to account for detection losses.
We introduce and experimentally implement a method for the detector calibration of photon-number-resolving time-bin multiplexing layouts based on the measured click statistics of superconducting nanowire detectors. In particular, the quantum efficiencies, the dark count rates, and the positive operator-valued measures of these measurement schemes are directly obtained with high accuracy. The method is based on the moments of the click-counting statistics for coherent states with different coherent amplitudes. The strength of our analysis is that we can directly conclude---on a quantitative basis---that the detection strategy under study is well described by a linear response function for the light-matter interaction and that it is sensitive to the polarization of the incident light field. Moreover, our method is further extended to a two-mode detection scenario. Finally, we present possible applications for such well-characterized detectors, such as sensing of atmospheric loss channels and phase sensitive measurements.
We report on the implementation of a time-multiplexed click detection scheme to probe quantum correlations between different spatial optical modes. We demonstrate that such measurement setups can uncover nonclassical correlations in multimode light fields even if the single mode reductions are purely classical. The nonclassical character of correlated photon pairs, generated by a parametric down-conversion, is immediately measurable employing the theory of click counting instead of low-intensity approximations with photoelectric detection models. The analysis is based on second- and higher-order moments, which are directly retrieved from the measured click statistics, for relatively high mean photon numbers. No data postprocessing is required to demonstrate the effects of interest with high significance, despite low efficiencies and experimental imperfections. Our approach shows that such novel detection schemes are a reliable and robust way to characterize quantum-correlated light fields for practical applications in quantum communications.
Abstract Though photon-number-resolving (PNR) detectors based on multiplexed threshold elements are key tools for quantum optics and quantum information, yet accurate calibration of their response in the presence of imperfections remains challenging. Here we develop a model for a four-channel PNR detector designed as a superconducting nanowire single-photon detector (SNSPD) array, allowing for unequal channel transmission coefficients and dark counts. Closed-form expressions for the click probabilities and transfer-matrix elements are obtained for coherent-state probes, and a numerical study quantifies the range of channel imbalance where the commonly used equal-channel, single-parameter approximation fails. Applying this framework to experimental data from a four-channel PNR SNSPD, we show that direct model-based fits do not reproduce the measured click statistics probably because of inter-channel cross-talks. To overcome this, we implement a hybrid quantum detector tomography scheme that combines a model-based fit to the mean click number with a data-driven reconstruction of the low-photon subspace. The resulting transfer matrix reproduces the experimental click statistics with average fidelity above 99.9% and provides a robust description of the detector in the presence of cross-talks and other non-idealities.
Direct estimation of g(2)(0)g^{(2)}(0)g(2)(0) from click statistics of a multiplexed detector
We present and theoretically analyze a method for direct estimation of the second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0) from the click statistics of a multiplexed detector composed of M binary on-off detection channels. The method uses linear estimators of the first and second moments of the photon-number operator and can provide accurate results even for optical fields with substantial mean photon numbers. For a fixed number of channels, the detection range can be extended by introducing additional losses before the detector. We demonstrate the performance of the method for coherent, thermal, amplitude-squeezed, and photon-added coherent states. We also derive a nonclassicality criterion based on the estimated correlation function and show how the method can be adapted to unbalanced detectors. Our work establishes direct estimation of g(2)(0)g^{(2)}(0)g(2)(0) as a simple and versatile method for quantitatively characterizing quantum light using multiplexed click detectors.
We derive an analytical description for quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation using correlated light fields, photon addition, and photon subtraction processes. Using a postselection procedure to a particular number of clicks of the detector system, the output states reveal a variety of quantum features. The rigorous description allows the identification and characterization of fundamentally unavoidable attenuations within given processes. We also generalize a known scenario of noiseless amplification with click detectors for the purpose of the preparation of various types of nonclassical states of light. Our exact results are useful for a choice of experimental parameters to realize a target state.
We investigate the use of a photon-number resolving (PNR) detector as an alternative method for measuring the second-order correlation function g2(0). Our implementation employs four spatially multiplexed single-photon detectors to reconstruct the photon number distribution P(n) from click statistics. We estimate g2(0) for both coherent and quantum dot excition emission, and compare the results to those obtained from a conventional Hanbury Brown-Twiss (HBT) setup. In the single-mode regime, we observe close agreement between both approaches. We additionally compare the acquisition times required for each method and find that PNR-based measurements enable faster estimation of g2(0), offering potential advantages for scalable characterisation of quantum light sources.