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Journal of the Optical Society of America B

Neural network method: withstanding noise for continuous-variable quantum key distribution with discrete modulation

Dingmin Cheng, Yewei Guo, Jiayang Dai, Hao Wu, Ying Guo

Published Feb 21, 2024• 1 citation
Publisher

Abstract

Excess noise in continuous-variable quantum key distribution systems usually results in a loss of key rate, leading to fatal security breaches. This paper proposes a long short-term memory time-sequence neural network to predict the key rate of the system while counteracting the effects of excess noise. The proposed network model, which can be updated with historical data, predicts the key rate of the future moment for the input time-sequence data. To increase the key rate, we perform a postselection operation to combat excess noise. We demonstrate the asymptotic security of the protocol against collective attacks with the numerical simulations using the quadrature phase-shift keying protocol, where some parameters have been optimized to resist excess noise. It provides a potential solution for improving the security of quantum communication in practical applications.

DOI
10.1364/josab.509184

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Excess noise in continuous-variable quantum key distribution systems usually results in a loss of key rate, leading to fatal security breaches. This paper proposes a long short-term memory time-sequence neural network to predict the key rate of the system while counteracting the effects of excess noise. The proposed network model, which can be updated with historical data, predicts the key rate of the future moment for the input time-sequence data. To increase the key rate, we perform a postselection operation to combat excess noise. We demonstrate the asymptotic security of the protocol against collective attacks with the numerical simulations using the quadrature phase-shift keying protocol, where some parameters have been optimized to resist excess noise. It provides a potential solution for improving the security of quantum communication in practical applications.
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.
Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.
Continuous-variable quantum key distribution (CV QKD) with discrete modulation has attracted increasing attention due to its experimental simplicity, lower-cost implementation and compatibility with classical optical communication. Correspondingly, some novel numerical methods have been proposed to analyze the security of these protocols against collective attacks, which promotes key rates over one hundred kilometers of fiber distance. However, numerical methods are limited by their calculation time and resource consumption, for which they cannot play more roles on mobile platforms in quantum networks. To improve this issue, a neural network model predicting key rates in nearly real time has been proposed previously. Here, we go further and show a neural network model combined with Bayesian optimization. This model automatically designs the best architecture of neural network computing key rates in real time. We demonstrate our model with two variants of CV QKD protocols with quaternary modulation. The results show high reliability with secure probability as high as 99.15% − 99.59%, considerable tightness and high efficiency with speedup of approximately 107 in both cases. This inspiring model enables the real-time computation of unstructured quantum key distribution protocols’ key rate more automatically and efficiently, which has met the growing needs of implementing QKD protocols on moving platforms.
Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices.However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks.In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying technique.By limiting information leakage, our proposed protocol enhances excess noise tolerance to a high level.Furthermore, we demonstrate that homodyne detection performs better than heterodyne detection in quaternary-modulated continuous-variable quantum key distribution under the untrusted detector noise scenario.The security is analyzed using the tight numerical method against collective attacks in the asymptotic regime.Our results imply that the current protocol can distribute keys in nearly intercity area and, thus, paves the way for constructing low-cost quantum secure communication networks.
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.
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.