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Physical Review Applied

Generalized Decoy-State Scheme for Rigorous Characterization of Single-Photon Detectors

Haibo Wang, Gong Zhang, Jishen Zhang, Chao Wang, Haiwen Xu, Yan Liang, Charles Ci Wen Lim, Xiao Gong

Published Sep 21, 2023• 0 citations
Publisher

Abstract

Accurate characterization of the single-photon detection efficiency (SPDE) of single-photon detectors (SPDs) is an essential but nontrivial task for various applications. Conventional methods require detailed detector models to calculate the estimated SPDE, which are not always available. To overcome this limitation, we propose a generalized method based on decoy state for accurate characterization of SPDE with experimental demonstration and verification in this work. The decoy-state scheme uses only three weak laser intensities to probe the response of an SPD and calculate rigorous bounds on the background noise and SPDE without prior knowledge of the detector model. To show the versatility, the decoy-state scheme is applied to the single-photon avalanche diode and the homodyne detector. The effects of time-dependent noise and multiphoton response to our scheme are analyzed. The experimental results show that the effects of time-dependent noise can be eliminated, and an accuracy bound of efficiency can be achieved with a bound range of 2.6%. The relaxed assumptions on the detector model, straightforward measurement process, rigorous calculation, and high accuracy, could open possibilities for our generalized toolbox as a device calibration standard, fundamental physics research, quantum information, lidar, and biomedical applications.

DOI
10.1103/physrevapplied.20.034049

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Accurate characterization of the single-photon detection efficiency (SPDE) of single-photon detectors (SPDs) is an essential but nontrivial task for various applications. Conventional methods require detailed detector models to calculate the estimated SPDE, which are not always available. To overcome this limitation, we propose a generalized method based on decoy state for accurate characterization of SPDE with experimental demonstration and verification in this work. The decoy-state scheme uses only three weak laser intensities to probe the response of an SPD and calculate rigorous bounds on the background noise and SPDE without prior knowledge of the detector model. To show the versatility, the decoy-state scheme is applied to the single-photon avalanche diode and the homodyne detector. The effects of time-dependent noise and multiphoton response to our scheme are analyzed. The experimental results show that the effects of time-dependent noise can be eliminated, and an accuracy bound of efficiency can be achieved with a bound range of 2.6%. The relaxed assumptions on the detector model, straightforward measurement process, rigorous calculation, and high accuracy, could open possibilities for our generalized toolbox as a device calibration standard, fundamental physics research, quantum information, lidar, and biomedical applications.
We introduce an experimental setup for measuring the detection efficiency of free-space single-photon detectors with excellent reproducibility and minimized uncertainty . Our analysis extends to account for the wavelength-dependent effects caused by the transmissivity of the optical window in front of the detector’s active area. The proposed approach involves measuring the detector’s response at different wavelengths and comparing it with a calibrated reference detector, enabling precise quantification of efficiency variations due to the optical window. The results provide a detailed understanding of wavelength-dependent efficiency, which is essential for optimizing the performance of single-photon detectors in applications such as quantum communication and photonics research. This characterization technique represents a significant step forward in enhancing the accuracy and reliability of single-photon detection efficiency measurements.
Single-photon detectors are a pivotal component in photonic quantum technologies. A precise and comprehensive calibration of the inherent detection efficiency is of utmost importance to ensure the proper evaluation of the performance in view of the specific technological application of interest, such as the protection against security breaches in quantum cryptographic solutions. Here we report on a systematic study and comprehensive analysis of the estimation of the inherent detection efficiency of two commercial single-photon detectors based on single-photon avalanche diodes for various mean photon numbers and at high laser pulse repetition rates using different techniques. We observe an unexpected and significant drop in the inherent detection efficiency at detection rates of 10% and higher relative to the maximum detection rate. It is demonstrated that for data analysis a statistical model for the detection rate conveniently can be used if no time-stamped data are available. We conclude that the full characterization of single-photon detectors used in critical applications should include the sensitivity of their inherent detection efficiency to high event rates.
In this paper, we present an experimental apparatus for the measurement of the detection efficiency of free-space single-photon detectors based on the substitution method. We extend the analysis to account for the wavelength dependence introduced by the transmissivity of the optical window in front of the detector's active area. Our method involves measuring the detector's response at different wavelengths and comparing it to a calibrated reference detector. This allows us to accurately quantify the efficiency variations due to the optical window's transmissivity. The results provide a comprehensive understanding of the wavelength-dependent efficiency, which is crucial for optimizing the performance of single-photon detectors in various applications, including quantum communication and photonics research. This characterization technique offers a significant advancement in the precision and reliability of single-photon detection efficiency measurements.
Single-photon detectors (SPDs) are ubiquitous in many protocols for quantum imaging, sensing, and communications. Many of these protocols critically depend on the precise knowledge of their detection efficiency. A method for the calibration of SPDs based on sources of quantum-correlated photon pairs uses single-photon detection to generate heralded single photons, which can be used as a standard of radiation at the single-photon level. These heralded photons then allow for precise calibration of SPDs in absolute terms. In this work, we investigate the absolute calibration of avalanche photodiodes based on a portable, commercial bi-photon source, and investigate the effects of multi-photon events from the spontaneous parametric down conversion (SPDC) process in these sources. We show that the multi-photon character of the bi-photon source, together with system losses, has a significant impact on the achievable accuracy for the calibration of SPDs. However, modeling the expected photon counting statistics from the squeezed vacuum in the SPDC process allows for accurate estimation of the efficiency of SPDs, assuming that the system losses are known. This study provides essential information for the design and optimization of portable bi-photon sources for their application in on-site calibration of SPDs with high accuracy, without requiring any other reference standard.
Quantum mechanics cements the intimate relationship between the nature of light and its detection. Historically, quantum theories of photodetection have generally fallen into two categories: the first tries to determine what quantum field observable is measured when photoelectrons are detected, laying the theoretical groundwork for photodetection being possible. The second type are phenomenological theories, which take great care to model the details of specific photodetectors. In this dissertation, we fill in the gap between these two models in the modern literature on photodetection by constructing a fully quantum-mechanical and sufficiently realistic model that includes all stages of the photodetection process. We accomplish this within the framework of quantum information theory using the language of positive operator valued measures (POVMs). \n\nA POVM provides the most general description of a quantum measurement. In the context of single-photon detection, the photodetector POVM provides a complete characterization of the single-photon detector (SPD) from which all figures of merit can be calculated. Each element of the POVM is comprised of a weighted sum over single-photon state projectors. To construct SPD POVMs, we identify the states projected onto by a measurement and the associated weights. We first accomplish this for a simple time-dependent system, laying out how to efficiently project onto arbitrary single-photon states. Then, we describe the three stages of a realistic SPD: transmission, amplification, and measurement.\n\nIn the transmission stage of photodetection a photon enters a network of discrete energy levels, its energy propagating through that network and finally exiting into another output continuum of modes, a process entirely described by a single complex function. In the amplification stage of photodetection, a single excitation is amplified into a macroscopic signal via a nonlinear amplification mechanism. In the final stage, an inefficient ``classical'' measurement is made on the macroscopic signal. By combining these three stages we form a chain of inference from the final ``click'' to the input photon and construct a POVM projecting onto the input Hilbert space. Lastly, we discuss limits and tradeoffs that arise at each stage and implications for photodetection applications.\n\nThis dissertation contains previously published and unpublished material.