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IEEE photonics journal

Neural Network-Powered Nonlinear Compensation Framework for High-Speed Continuous Variable Quantum Key Distribution

Hang Zhang, Yong Luo, Ling Zhang, Xinchao Ruan, Duan Huang

Published Apr 19, 2022• 5 citations
Publisher

Abstract

In this paper, we present a neural network-based framework to compensate for the nonlinear distortion of high-speed continuous variable quantum key distribution (CV-QKD) systems. In practice, the nonlinear impairment of imperfect devices could bring interference to the measured quadrature values and thus compromise the parameter estimation procedure and the secure key rate. Specifically, for a high-speed CV-QKD system, the balanced homodyne detector (BHD) and the following analog-to-digital converter are the primary sources of nonlinear impairment. The nonlinear distortion effect will be more pronounced as the pulse repetition rate increases. We propose an autoencoder-based network to learn the inner patterns of distorted data and then compensate the quadrature measurements in real-time at the receiver’s side. The numerical simulation demonstrates that the excess noise induced by nonlinear impairment is reduced to the$10^{-3}$level in the shot noise unit. Consequently, such a software approach has the ability to significantly boost the bandwidth efficiency of the BHD and the secure key bit rate.

DOI
10.1109/jphot.2022.3167760

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In this paper, we present a neural network-based framework to compensate for the nonlinear distortion of high-speed continuous variable quantum key distribution (CV-QKD) systems. In practice, the nonlinear impairment of imperfect devices could bring interference to the measured quadrature values and thus compromise the parameter estimation procedure and the secure key rate. Specifically, for a high-speed CV-QKD system, the balanced homodyne detector (BHD) and the following analog-to-digital converter are the primary sources of nonlinear impairment. The nonlinear distortion effect will be more pronounced as the pulse repetition rate increases. We propose an autoencoder-based network to learn the inner patterns of distorted data and then compensate the quadrature measurements in real-time at the receiver’s side. The numerical simulation demonstrates that the excess noise induced by nonlinear impairment is reduced to the10−310^{-3}10−3level in the shot noise unit. Consequently, such a software approach has the ability to significantly boost the bandwidth efficiency of the BHD and the secure key bit rate.
Continuous-variable quantum key distribution (CV-QKD) with discrete modulation has received widespread attentions because of its experimental simplicity, lower-cost implementation and ease to multiplex with classical optical communication. Recently, some inspiring numerical methods have been applied to analyse the security of discrete-modulated CV-QKD against collective attacks, which promises to obtain considerable key rate over one hundred kilometers of fiber distance. However, numerical methods require up to ten minutes to calculate a secure key rate one time using a high-performance personal computer, which means that extracting the real-time secure key rate is impossible for discrete-modulated CV-QKD system. Here, we present a neural network model to quickly predict the secure key rate of homodyne detection discrete-modulated CV-QKD with good accuracy based on experimental parameters and experimental results. With the excess noise of about 0.010.010.01, the speed of our method is improved by about seven orders of magnitude compared to that of the conventional numerical method. Our method can be extended to quickly solve complex security key rate calculation of a variety of other unstructured quantum key distribution protocols.
In continuous-variable quantum key distribution (CV-QKD), the key information are encoded on quadratures of the optical field, which are measured via balanced homodyne detector (BHD). The bandwidth of the BHD is one of key parameters for precise characterization of quantum states. We establish a theoretical model to analyze the impact of the BHD bandwidth and signal modulation patterns on the channel parameters estimation of CV-QKD systems. Based on the proposed model, the secure key rate of a practical CV-QKD system under different BHD bandwidths and signal modulation patterns are investigated. Our results show that insufficient BHD bandwidth will result in wrong estimate of the transmission loss and excess noise, which significantly affects the performance of CV-QKD systems. Given the BHD bandwidth, there exists an optimal signal repetition rate that maximizes the secure key rate. The BHD bandwidth requirement of the QKD system increases with the transmission distance for large duty cycle pulse. Furthermore, the root raised-cosine pulse signal modulation performs better than the square pulse signal modulation in general.
Abstract Numerical methods are widely used to calculate the secure key rate of many quantum key distribution protocols in practice, but they consumes many computing resources and are too time-consuming. In this work, we take the homodyne detection discrete-modulated continuous-variable quantum key distribution (CV-QKD) as an example, and construct a neural network that can quickly predict the secure key rate based on the experimental parameters and experimental results. Compared to traditional numerical methods, the speed of the neural network is improved by several orders of magnitude. Importantly, the predicted key rates are not only highly accurate but also highly likely to be secure. This allows the secure key rate of discrete-modulated CV-QKD to be extracted in real time on a low-power platform. Furthermore, our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols.
Abstract Parameter estimation is a critical step in continuous-variable quantum key distribution (CV-QKD), as the statistical uncertainty from a finite data size leads to pessimistic worst-case bounds that drastically reduce the secret key rate and range. While machine learning techniques have been proposed for this task, they have lacked the rigorous statistical framework necessary for integration into a composable security proof. In this work, we bridge this gap by introducing a statistically rigorous framework for using neural networks for parameter estimation in CV-QKD with quantifiable composable security. We develop a neural network estimator for the excess noise and, crucially, derive its worst-case confidence interval using a delta method approach, ensuring the estimation fails with a probability not exceeding ε PE . This allows the network to be integrated into a parameter estimation protocol that is operationally equivalent to the standard maximum likelihood method but yields significantly tighter parameter bounds. Our numerical results demonstrate that this method provides substantially more precise estimates, which directly translates into a higher secret key rate and extended transmission distance over a fiber channel under a collective Gaussian attack. This work establishes that machine learning can be securely and effectively harnessed to overcome a key performance limitation in practical CV-QKD systems.
Numerical methods are widely used to calculate the secure key rate of many quantum key distribution protocols in practice, but they consume many computing resources and are too time-consuming. In this work, we take the homodyne detection discrete-modulated continuous-variable quantum key distribution (CV-QKD) as an example, and construct a neural network that can quickly predict the secure key rate based on the experimental parameters and experimental results. Compared to traditional numerical methods, the speed of the neural network is improved by several orders of magnitude. Importantly, the predicted key rates are not only highly accurate but also highly likely to be secure. This allows the secure key rate of discrete-modulated CV-QKD to be extracted in real time on a low-power platform. Furthermore, our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols.
Abstract In the continuous-variable quantum key distribution (CV-QKD) system, the secure key rate and the throughput of secure keys are important factors in measuring system quality. However, the secure key rate and the throughput of secure keys depend on various nonlinearly related parameters, which makes it difficult to effectively find the optimal parameters. In this paper, we introduce machine learning into the CV-QKD system and propose a parameter optimization scheme for the CV-QKD system based on the back-propagation (BP) neural network. The proposed scheme improves the secure key rate and throughput of secure keys by optimizing the code rate and the number of decoding iterations in the error correction process. Furthermore, under some reasonable assumptions, we prove that the optimization objective is a concave function of the optimization parameters under the BP neural network, which ensures that there exists a global optimal solution in a certain domain and provides a theoretical basis for the optimization based on BP neural networks. Simulation results show that compared with traditional optimization schemes, the proposed scheme can improve the secure key rate and transmission distance.