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Physical Review Applied

Realistic detector model for a time-bin-encoding quantum key distribution system

Xiaojuan Huang, Ze-Hao Wang, Jia-Lin Chen, Feng-Yu Lu, Shuang Wang, Zhen−Qiang Yin, Jiaqi Geng, Wei Chen, De‐Yong He, Guan‐Jie Fan‐Yuan, Yu Wang, Guang‐Can Guo, Zheng‐Fu Han

Published May 27, 2025• 1 citation
Publisher

Abstract

In light of the growing widely utilized single-photon avalanche detectors, dead time is inevitable due to the presence of afterpulse. Dead time is a critical factor that influences the count rate and the secret key rate (SKR) of quantum key distribution (QKD). It is particularly significant in time-bin-encoding systems, while prior models fail to accurately estimate the gains. Of note, it introduces correlations between early bins and late bins, hence bits with strong correlation and security risks. Here, we put forward a realistic model that precisely characterizes the response of detectors for time-bin-encoding systems. Our model not only improves the accuracy of gain predictions, showing an excellent match with the Monte Carlo simulation results, but also provides theoretical support for data processing, helping to mitigate security risks. Finally, leveraging our model, we can get a much higher SKR than prior models and further enhance the performance of practical QKD systems by adjusting the detector parameters. Our simulation results demonstrate that our model is essential for the application and deployment of QKD systems in practice.

DOI
10.1103/physrevapplied.23.054071

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In light of the growing widely utilized single-photon avalanche detectors, dead time is inevitable due to the presence of afterpulse. Dead time is a critical factor that influences the count rate and the secret key rate (SKR) of quantum key distribution (QKD). It is particularly significant in time-bin-encoding systems, while prior models fail to accurately estimate the gains. Of note, it introduces correlations between early bins and late bins, hence bits with strong correlation and security risks. Here, we put forward a realistic model that precisely characterizes the response of detectors for time-bin-encoding systems. Our model not only improves the accuracy of gain predictions, showing an excellent match with the Monte Carlo simulation results, but also provides theoretical support for data processing, helping to mitigate security risks. Finally, leveraging our model, we can get a much higher SKR than prior models and further enhance the performance of practical QKD systems by adjusting the detector parameters. Our simulation results demonstrate that our model is essential for the application and deployment of QKD systems in practice.
A precise estimation of the detection response is essential for a high-performance and secure quantum-key-distribution (QKD) system. Single-photon avalanche diodes (SPADs) are widely applied to estimate the single-photon yields. However, in the presence of the dead time and afterpulse of the SPADs, the estimations of gains in previous models are biased, which will lead to ill-fitting optimized parameters and greatly degrade the system performance. Here, we develop a dependency model for providing more accurate optimization to achieve higher-performance QKD systems. Moreover, to further improve the system performance, our model guides users to choose proper dead time. Our simulation results indicate that our model plays an important role in the practical application and deployment of QKD systems.
High-dimensional quantum resources provide the ability to encode several bits of information on a single photon, which can particularly increase the secret key rate rate of quantum key distribution (QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations. Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.
There has been growing research interest in quantum technology in general and in quantum key distribution (QKD) in particular. However, the key generation rate of QKD systems is still limited by the quantum channel losses as well as the practical limitations of the quantum sources and detectors. Here, we focus on one of these limitations, namely, the quantum detector's dead time effect, which happens after each photon detection, limiting the maximum quantum bit transmission rate and consequently the key generation rate of QKD systems. Qubit transmission at the sub-dead-time regime (i.e., faster than the reciprocal of dead time) can introduce different security loopholes. In this paper, we propose the use of a detector array instead of a single detector to measure the quantum state of individual photons in discrete variable QKD systems, showing that it can significantly alleviate the limitations induced by detectors' dead time. A dead-time compensated BB84 scheme is introduced, allowing qubit transmission at the sub-dead-time regime. AnM−M-M−dimensional Markov chain model is used to describe the impact of dead time on the operation of the proposed BB84 system, employing detector arrays of sizeMMM. Consequently, novel analytical expressions can be derived for the sifted bit rate (SBR) and secrecy key rate (SKR) of the proposed QKD system, showing excellent match with the Monte Carlo simulation results. A remarkable gain is observed for the BB84 system employing detector arrays, showing a potentialMMM-fold improvement of SBR at high qubit transmission rates.
Quantum-key-distribution (QKD) protocols that rely on coincidence events registered with two or more detectors are prone to detector saturation effects due to detector dead times. In particular, systems using avalanche photodiodes may incur a reduction in the achievable secret key rate. We demonstrate a detector gating scheme tuned to mitigate these effects but keep the detectors in an otherwise free-running mode. When a first detector is inactive due to a previous detection, other unfavorable detection events in a second detector are blocked, as they would not contribute to the key but just lead to another dead time. We implement this method by synchronizing the detectors’ dead time in our time-bin entanglement QKD system and demonstrate its feasibility for various fiber link distances and detector settings, increasing the sifted key rate by up to 78% with no significant change in the quantum bit error rate.
Recently, there has been growing research interest in quantum technology in general and particularly in quantum key distribution (QKD) that enables two legitimate parties to share a secret key without leaking information to third parties. Practical implementation of QKD has shown limited key rates due to the practical limits of quantum sources and detectors. For example, after each detection event, practical single-photon detectors such as single-photon avalanche diodes (SPADs) undergo a period of inactivity called dead time, which limits the highest photon transmission rate achievable for QKD systems as photon transmission at sub-dead-time regime can generate security loopholes. In this paper, we analyze the performance of a sifting scheme that allows for high-speed operation at sub-dead-time regime both theoretically and numerically. We consider an FSO QKD system, where the effect of background noise can be significant and derive the expressions of sifting probability and sifted bit rate considering both dead time and background noise effects. We present a comprehensive performance analysis of the QKD system in terms of quantum bit error rate (QBER) and secrecy key rate (SKR) and show that operation at sub-dead-time regime can significantly improve the achievable SKR for FSO systems with certain path loss and background noise levels.
Higher Dimensional Quantum Key Distribution (HD-QKD) improves information capacity and security compared to binary QKD systems. Previous HD-QKD implementations have required d+1 (d refers to encoding dimension) single-photon detectors, limiting large-scale implementation. In contrast, another HD-QKD implementation using coherent one-way (COW) protocol hardware with two detectors achieved a secret key rate (SKR) of 155 kbps for an 8-D system and 2.7% QBER tolerance for a 16-D system with qubit scrambling across a time window. In this paper, we theoretically simulate and experimentally demonstrate time-bin encoded HD-QKD using COW protocol hardware with two single-photon detectors operating at standard telecom wavelengths, achieving a remarkable maximum encoding of 6 bits per photon (i.e., 56-d system). Our HD-QKD system incorporates a practical decoy-state technique to counter the photon number splitting attack, allowing greater flexibility in choosing higher mean photon number thereby achieving higher SKR and distances. This implementation demonstrates a remarkable ninefold increase in SKR for a 16-d system (210 kbps over 25 km of standard single-mode fiber) compared to qubit-based systems, with a QBER tolerance of 13.5% for d = 16. Notably, we achieved positive key rates for emulated loss up to 131 km of fiber length for d = 8. By optimizing detector deadtime and mean photon number using our theoretical model, we achieve enhanced key rates and security. Our findings highlight the superiority of our approach and lay the foundation for high throughput HD-QKD implementation, offering a secure and efficient method for transmitting sensitive information.