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arXiv:2303.13742

Dead-time optimization to increase secure distance range in prepare and measure quantum key distribution protocols

Carlos Wiechers, J. L. Lucio, Xóchitl Sánchez-Lozano, Rafael Gómez-Medina, Mariana Salado-Mejía

Published Mar 24, 2023• 0 citations
arXivHTMLPDF

Abstract

Afterpulsing is a factor limiting the distance over which discrete-variable quantum key distribution systems are secure, and a common feature in single-photon detectors. The relevance of this phenomenon stems from its stochastic, self-interacting nature and the fact that its rate rises with the number of avalanche events, which increases the quantum bit error rate. Here we introduce an effective analytic model, including dead-time and afterpulsing corrections, where afterpulsing correction depends on dead-time value. This model is useful to evaluate the performance of prepare and measure quantum key distribution protocols (standard and decoy versions) that use gated single photon detectors. The model provides an expression to numerically optimize the secret key rate over the full distance range for secure communication, enabling in this way the calculation of quantum bit error rate and secure key rate. In the conventional procedure, the dead-time value is fixed regardless of distance, limiting the distance range of the channel due to remaining afterpulsing effects, which are more relevant at higher operating frequencies. Here we demonstrate that optimizing the dead-time values increases the distance range of the channel to share secret keys.

DOI
10.48550/arxiv.2303.13742

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Afterpulsing is a factor limiting the distance over which discrete-variable quantum key distribution systems are secure, and a common feature in single-photon detectors. The relevance of this phenomenon stems from its stochastic, self-interacting nature and the fact that its rate rises with the number of avalanche events, which increases the quantum bit error rate. Here we introduce an effective analytic model, including dead-time and afterpulsing corrections, where afterpulsing correction depends on dead-time value. This model is useful to evaluate the performance of prepare and measure quantum key distribution protocols (standard and decoy versions) that use gated single photon detectors. The model provides an expression to numerically optimize the secret key rate over the full distance range for secure communication, enabling in this way the calculation of quantum bit error rate and secure key rate. In the conventional procedure, the dead-time value is fixed regardless of distance, limiting the distance range of the channel due to remaining afterpulsing effects, which are more relevant at higher operating frequencies. Here we demonstrate that optimizing the dead-time values increases the distance range of the channel to share secret keys.
Abstract In order to clarify how the generation of afterpulses in single‐photon detectors based on InGaAs avalanche photodiodes affects quantum key distribution based on the BB84 protocol, we have evaluated the dependence of the final keyrate on the detector clock frequency synchronized between the sender and the receiver, the mean photon number of the incident light pulse from the sender, and the propagation distance between the sender and the receiver. In calculating the quantum bit error rate (QBER), we used measured values for the dark‐count probability and the afterpulse probability. In calculating the keyrate per pulse, we used the conditions described by Lütkenhaus for unconditionally secure quantum key distribution. The results of our analysis reveal that the maximum value of the keyrate when considering the effect of the afterpulses was decreased by about a factor of 1/2 from its value when neglecting the effect of afterpulses. It is also found that there exist optimal operating conditions (mean photon number and clock frequency) for maximizing the keyrate, and that in order to determine these conditions it is essential to take into account the effect of afterpulses. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(9): 38–45, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjb.20059
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.
The passive decoy method, a candidate for high-speed quantum key distribution (QKD), can prepare laser pulses with various photon-number distributions according to the responses of the transmitter's detectors, which usually adopts the single-photon avalanche photodiode (SPAD) in QKD. As an intrinsic characteristic of the SPAD, the afterpulse can introduce random detector responses, however, is regrettably ignored in passive schemes. Here we develop an analytical model for passive schemes in the finite-resource regime to describe the afterpulse effect on the detectors of both transmitter and receiver. The photon-number distributions biased by afterpulses are corrected, which reveals that the secure key rate is significantly overrated when the afterpulse is ignored. Moreover, our model can increase the tolerance of passive decoy source to afterpulse effect as the result shows that the secret key rates are comparable at different afterpulse probability by reoptimization.
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.
Twin-field quantum key distribution (TF-QKD) surpasses the repeaterless key-rate bound, offering great promise for long-distance quantum communication. Avalanche-photodiode (APD) single-photon detectors are widely used in practical QKD systems, due to their compactness, cost-effectiveness, and room-temperature operation. However, their non-ideal characteristics-including afterpulse probability, dead time, and dark counts-can severely degrade TF-QKD performance. In this work, we develop a comprehensive TF-QKD simulation model incorporating these APD imperfections, enabling quantitative analysis of their individual impacts. Our results reveal that afterpulse induced by high-intensity reference pulses is the dominant performance-limiting factor. Under identical APD conditions, we compare three representative TF-QKD protocols. The sending-or-not-sending (SNS) protocol demonstrates superior long-distance performance due to its higher signal photon number and enhanced noise tolerance. This study provides practical guidance for the design of compact, APD-based TF-QKD systems and highlights key strategies for performance optimization.
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.