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Physical Review Applied

Afterpulse Analysis for Quantum Key Distribution

Guan‐Jie Fan‐Yuan, Chao Wang, Shuang Wang, Zhen−Qiang Yin, He Liu, Wei Chen, De‐Yong He, Zheng‐Fu Han, Guang‐Can Guo

Published Dec 13, 2018• 52 citations
Publisher

Abstract

In optical quantum cryptography, the afterpulse effect is important for secure key generation in quantum key distribution (QKD), because it introduces additional error and leads to great deviation from the traditional analytical model, especially for high-speed systems. This study develops a different analytical model to make QKD systems more afterpulse-compatible, by exploiting the non-Markovian nature of the afterpulse. The optimized key rate obtained here is much higher, and thus the tolerance of the afterpulse effect can be significantly improved in practical QKD systems for secure communication.

DOI
10.1103/physrevapplied.10.064032

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In optical quantum cryptography, the afterpulse effect is important for secure key generation in quantum key distribution (QKD), because it introduces additional error and leads to great deviation from the traditional analytical model, especially for high-speed systems. This study develops a different analytical model to make QKD systems more afterpulse-compatible, by exploiting the non-Markovian nature of the afterpulse. The optimized key rate obtained here is much higher, and thus the tolerance of the afterpulse effect can be significantly improved in practical QKD systems for secure communication.
There is no doubt that measurement-device-independent quantum key distribution (MDI-QKD) is a crucial protocol that is immune to all possible detector side channel attacks. In the preparation phase, a simulation model is usually employed to get a set of optimized parameters, which is utilized for getting a higher secure key rate in reality. With the implementation of high-speed QKD, the afterpulse effect which is an intrinsic characteristic of the single-photon avalanche photodiode is no longer ignorable, this will lead to a great deviation compared with the existing analytical model. Here we develop an afterpulse-compatible MDI-QKD model to get the optimized parameters. Our results indicate that by using our afterpulse-compatible model, we can get a much higher key rate than the prior afterpulse-omitted model. It is significant to take the afterpulse effect into consideration because of the improvement of the system working frequency.
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.
The round-robin differential phase shift (RRDPS) quantum key distribution (QKD) protocol is the only one that does not require monitoring of signal disturbance. Moreover, it has been proven that RRDPS has excellent performance of resistance to finite-key effects and high error rate tolerance. However, the existing theories and experiments do not take the afterpulse effects into account, which cannot be neglected in high-speed QKD systems. Here, we propose a tight finite-key analysis with afterpulse effects. The results show that the non-Markovian afterpulse RRDPS model optimizes the system performance considering afterpulse effects. The advantage of RRDPS over decoy-state BB84 under short-time communication still holds at typical values of afterpulse.
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.
The most important goal of quantum communication is to distribute the encryption key between the transmitter and the receiver. The optimal situation in Quantum Key Distribution (QKD) between transmitter and receiver is to increase the key distribution rate per second, increase the transmission distance, and reduce the error in key distribution. Several protocols used for QKD. The most important of QKD protocols is the BB84. One of the challenges leading to errors in quantum protocols is generating error pulses in single-photon detectors. These pulses caused by the inherent effects of quantum devices. They can cause wrong detection in the receiver. Many measures have been taken in the design and construction of single-photon detectors to reduce this error pulses, but it is not possible to eliminate all of them. Afterpulse and dark counts are two types of unwanted pulses that occur with single-photon detectors. In this paper, a new QKD protocol is proposed. It is an upgrade of the BB84 protocol and can reduce the effects of unwanted pulses such as afterpulse and dark counts in QKD avalanche detectors.
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.