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Applied Optics

Reducing the afterpulse effect in QKD systems using detector doubling in the BB84 protocol

Mahdi Rahmanpour, Alireza Erfanian, Ahmad Afifi, Mahdi Khaje, Mohammad Hossein Fahimifar

Published Jun 17, 2025• 2 citations
Publisher

Abstract

The afterpulse effect is an undesirable phenomenon that occurs in single-photon avalanche diodes (SPADs). SPADs are widely employed in quantum key distribution (QKD) systems. As QKD systems advance to support higher data rates, the minimization of afterpulses becomes increasingly critical. In this paper, we introduce what we believe to be a new structure for the BB84 QKD protocol to reduce afterpulses in QKD systems. The proposed method does not change the secure key rate compared to the conventional BB84 protocol. We conduct a theoretical analysis and simulation of the performance of a single-photon-based QKD system utilizing SPADs with suboptimal afterpulse characteristics. Our results indicate that the afterpulse probability (Pa) in SPADs does not impose a strict lower bound on the error rate of sifted keys in single-photon-based QKD systems. The system utilizes a simplified version of the two-bases BB84 protocol, which operates over fiber-optic or free-space channels. In the proposed structure, eight detectors are used to measure four polarization angles, yielding four possible outcomes. The findings emphasize the practicality of this setup for both fiber-based and free-space quantum communication, making it highly suitable for real-world applications. The afterpulse decay is dependent on an exponential function and changes proportionally to the elapsed time, the number of trapped carriers, the carrier lifetime, the field strength, and the temperature. The project team has extensive experience in afterpulse reduction and has published several papers on the subject. Using the idea presented in this paper, by doubling the receiver detectors under the same conditions, the probability of afterpulse occurrence is approximately halved. We are looking to propose new structures and protocols to reduce undesired pulses in single-photon avalanche detectors.

DOI
10.1364/ao.557367

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The afterpulse effect is an undesirable phenomenon that occurs in single-photon avalanche diodes (SPADs). SPADs are widely employed in quantum key distribution (QKD) systems. As QKD systems advance to support higher data rates, the minimization of afterpulses becomes increasingly critical. In this paper, we introduce what we believe to be a new structure for the BB84 QKD protocol to reduce afterpulses in QKD systems. The proposed method does not change the secure key rate compared to the conventional BB84 protocol. We conduct a theoretical analysis and simulation of the performance of a single-photon-based QKD system utilizing SPADs with suboptimal afterpulse characteristics. Our results indicate that the afterpulse probability (Pa) in SPADs does not impose a strict lower bound on the error rate of sifted keys in single-photon-based QKD systems. The system utilizes a simplified version of the two-bases BB84 protocol, which operates over fiber-optic or free-space channels. In the proposed structure, eight detectors are used to measure four polarization angles, yielding four possible outcomes. The findings emphasize the practicality of this setup for both fiber-based and free-space quantum communication, making it highly suitable for real-world applications. The afterpulse decay is dependent on an exponential function and changes proportionally to the elapsed time, the number of trapped carriers, the carrier lifetime, the field strength, and the temperature. The project team has extensive experience in afterpulse reduction and has published several papers on the subject. Using the idea presented in this paper, by doubling the receiver detectors under the same conditions, the probability of afterpulse occurrence is approximately halved. We are looking to propose new structures and protocols to reduce undesired pulses in single-photon avalanche detectors.
The afterpulse effect is an undesirable phenomenon that occurs in single-photon avalanche diodes (SPADs). SPADs are widely employed in quantum key distribution (QKD) systems. As QKD systems advance to support higher data rates, the minimization of afterpulses becomes increasingly critical. In this paper, we introduce new structure for BB84 QKD protocol to reduce afterpulses in QKD systems. The proposed method does not change secure key rate compared to the conventional BB84 protocol. We conduct a theoretical analysis and simulation of the performance of a single-photon-based QKD system utilizing SPADs with suboptimal afterpulse characteristics. Our results indicate that the afterpulse probability (Pa) in SPADs does not impose a strict lower bound on the error rate of sifted keys in single-photon-based QKD systems. The system utilizes a simplified version of the two-bases BB84 protocol, which operates over fiber-optic or free-space channels. In the proposed structure, eight detectors are used to measure four polarization angles, yielding four possible outcomes. The findings emphasize the practicality of this setup for both fiber-based and free-space quantum communication, making it highly suitable for real-world applications. The afterpulse decay is dependent on an exponential function and changes proportionally to the elapsed time, the number of trapped carriers, the carrier lifetime, the field strength, and the temperature. The project team has extensive experience in afterpulse reduction and has published several papers on the subject. Using the idea presented in this paper, by doubling the receiver detectors under the same conditions, the probability of afterpulse occurrence is approximately halved. We are looking to propose new structures and protocols to reduce undesired pulses in single-photon avalanche detectors.
The afterpulse effect is an undesirable phenomenon that occurs in single-photon avalanche diodes (SPADs). SPADs are widely employed in quantum key distribution (QKD) systems. As QKD systems advance to support higher data rates, the minimization of afterpulses becomes increasingly critical. In this paper, we introduce new structure for BB84 QKD protocol to reduce afterpulses in QKD systems. The proposed method does not change secure key rate compared to the conventional BB84 protocol. We conduct a theoretical analysis and simulation of the performance of a single-photon-based QKD system utilizing SPADs with suboptimal afterpulse characteristics. Our results indicate that the afterpulse probability (Pa) in SPADs does not impose a strict lower bound on the error rate of sifted keys in single-photon-based QKD systems. The system utilizes a simplified version of the two-bases BB84 protocol, which operates over fiber-optic or free-space channels. In the proposed structure, eight detectors are used to measure four polarization angles, yielding four possible outcomes. The findings emphasize the practicality of this setup for both fiber-based and free-space quantum communication, making it highly suitable for real-world applications. The afterpulse decay is dependent on an exponential function and changes proportionally to the elapsed time, the number of trapped carriers, the carrier lifetime, the field strength, and the temperature. The project team has extensive experience in afterpulse reduction and has published several papers on the subject. Using the idea presented in this paper, by doubling the receiver detectors under the same conditions, the probability of afterpulse occurrence is approximately halved. We are looking to propose new structures and protocols to reduce undesired pulses in single-photon avalanche detectors.
The afterpulse effect is an undesirable phenomenon that occurs in single-photon avalanche diodes (SPADs). SPADs are widely employed in quantum key distribution (QKD) systems. As QKD systems advance to support higher data rates, the minimization of afterpulses becomes increasingly critical. In this paper, we introduce new structure for BB84 QKD protocol to reduce afterpulses in QKD systems. The proposed method does not change secure key rate compared to the conventional BB84 protocol. We conduct a theoretical analysis and simulation of the performance of a single-photon-based QKD system utilizing SPADs with suboptimal afterpulse characteristics. Our results indicate that the afterpulse probability (Pa) in SPADs does not impose a strict lower bound on the error rate of sifted keys in single-photon-based QKD systems. The system utilizes a simplified version of the two-bases BB84 protocol, which operates over fiber-optic or free-space channels. In the proposed structure, eight detectors are used to measure four polarization angles, yielding four possible outcomes. The findings emphasize the practicality of this setup for both fiber-based and free-space quantum communication, making it highly suitable for real-world applications. The afterpulse decay is dependent on an exponential function and changes proportionally to the elapsed time, the number of trapped carriers, the carrier lifetime, the field strength, and the temperature. The project team has extensive experience in afterpulse reduction and has published several papers on the subject. Using the idea presented in this paper, by doubling the receiver detectors under the same conditions, the probability of afterpulse occurrence is approximately halved. We are looking to propose new structures and protocols to reduce undesired pulses in single-photon avalanche detectors.
A Single-Photon Avalanche Diode (SPAD) is a specialized optoelectronic device designed for the detection of single photons. It can discern the presence or absence of photons as well as their reception frequency. A significant challenge associated with SPADs is the generation of unintended pulses, which manifest in two primary categories: Dark Count Rate (DCR) and Afterpulse Probability (PAP). Dark counting refers to the occurrence of output pulses in the absence of photon detection, while afterpulse are undesirable outputs resulting from the trapping of carrier’s post-avalanche event within the detector. These trapped carriers are subsequently accelerated by the activation field applied to the detector, causing another avalanche breakdown known as an afterpulse. Both the afterpulse effect and dark counting are considered detrimental phenomena in SPADs, which are commonly utilized in Quantum Key Distribution (QKD) systems. Quantum Key Distribution is a cryptographic method for securely distributing secret keys, leveraging principles of quantum mechanics. Moreover, this method ensures that an eavesdropper cannot intercept or regenerate photon states. In this study, a novel approach is proposed to detect errors induced by these undesirable pulses in a quantum key distribution system. The proposed method, designed to mitigate the effects of unwanted pulses in QKD using the BB84 protocol, employs two quantum channels for photon transmission and a classical channel for coordination between the communicating parties and filtering the secret key (sifting). This method preserves the secure key rate when compared to the traditional BB84 protocol. The reduction of undesirable pulses in the proposed method is contingent upon factors such as the probability of afterpulse occurrence, dark count events, and the efficiency of the single-photon detector, with the reduction being computed in direct proportion to these parameters.
In this paper, we introduce a new Quantum Key Distribution (QKD) protocol designed to reduce afterpulsing by at least 55%. We provide both theoretical analysis and simulation results for a single-photon QKD system using SPADs that exhibit less-than-ideal afterpulse behavior. Our findings show that the afterpulse probability (P AP ) in SPADs does not set a strict lower limit on the error rate of sifted keys in single-photon QKD systems. The system uses a simplified two-state version of the BB84 protocol, with quantum states encoded in different polarizations over fiber or free-space channels. The protocol ensures that consecutive photons have distinct polarizations. In the enhanced protocol, four detectors measure two polarization bases, yielding four possible detection outcomes. The results demonstrate the practical potential of this approach for both fiber-optic and free-space quantum communication, making it especially suitable for real-world deployment. This work paves the way for developing new protocols in quantum communications. In the new method, by avoiding the transmission of two consecutive photons with the same polarization angle, the security level of the optimal BB84 protocol against attacks will be reduced to that of the B92 protocol. Simulations conducted in MATLAB and OptiSystem, under realistic conditions (1550 nm wavelength, InGaAs SPAD parameters: η = 30%, DCR = 10%, clock rate = 100 MHz), demonstrate a drop in afterpulse probability from 53% to 23.2%. The main advantages of the new protocol method over hardware-based methods are lower cost and no need for extensive hardware modifications. Additionally, using the optimized protocol alongside other methods to reduce afterpulse probability further decreases its occurrence.
A Single-Photon Avalanche Diode (SPAD) is a specialized optoelectronic device designed for the detection of single photons. It can discern the presence or absence of photons as well as their reception frequency. A significant challenge associated with SPADs is the generation of unintended pulses, which manifest in two primary categories: Dark Count Rate (DCR) and Afterpulse Probability (PAP). Dark counting refers to the occurrence of output pulses in the absence of photon detection, while afterpulse are undesirable outputs resulting from the trapping of carrier’s post-avalanche event within the detector. These trapped carriers are subsequently accelerated by the activation field applied to the detector, causing another avalanche breakdown known as an afterpulse. Both the afterpulse effect and dark counting are considered detrimental phenomena in SPADs, which are commonly utilized in Quantum Key Distribution (QKD) systems. Quantum Key Distribution is a cryptographic method for securely distributing secret keys, leveraging principles of quantum mechanics. Moreover, this method ensures that an eavesdropper cannot intercept or regenerate photon states. In this study, a novel approach is proposed to detect errors induced by these undesirable pulses in a quantum key distribution system. The proposed method, designed to mitigate the effects of unwanted pulses in QKD using the BB84 protocol, employs two quantum channels for photon transmission and a classical channel for coordination between the communicating parties and filtering the secret key (sifting). This method preserves the secure key rate when compared to the traditional BB84 protocol. The reduction of undesirable pulses in the proposed method is contingent upon factors such as the probability of afterpulse occurrence, dark count events, and the efficiency of the single-photon detector, with the reduction being computed in direct proportion to these parameters.