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Entropy

Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel

Yun Jie Mao, Yiwu Zhu, Hui Hu, Gaofeng Luo, Jinguang Wang, Yijun Wang, Ying Guo

Published Jun 14, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.3390/e25060937

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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.
The goal of continuous variable quantum key distribution (CVQKD) is to be diffusely used and adopted in diverse scenarios, so the adhibition of atmospheric channel will play a crucial part in constituting global secure quantum communications. Atmospheric channel transmittance is affected by many factors and does not vary linearly, leading to great changes in signal-to-noise ratio. It is crucial to choose the appropriate modulation variance under different turbulence intensities to acquire the optimal secret key rate. In this paper, the four-state protocol, back-propagation neural network (BPNN) algorithm was discussed in the proposed scheme. We employ BPNN to CVQKD, which could adjust the modulation variance to an optimum value for ensuring the system security and making the system performance optimal. The numerical results show that the proposed scheme is equipped to improve the secret key rate efficiently.
Continuous-variable quantum key distribution (CVQKD) allows legitimate parties to extract and exchange secret keys. However, the tradeoff between the secret key rate and the accuracy of parameter estimation still around the present CVQKD system. In this paper, we suggest an approach for parameter estimation of the CVQKD system via artificial neural networks (ANN), which can be merged in post-processing with less additional devices. The ANN-based training scheme, enables key prediction without exposing any raw key. Experimental results show that the error between the predicted values and the true ones is in a reasonable range. The CVQKD system can be improved in terms of the secret key rate and the parameter estimation, which involves less additional devices than the traditional CVQKD system.
There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) over an underwater link. In particular, we focus on analyzing the channel transmittance and detection efficiency based on Monte Carlo simulation for different water types, link distances and transceiver parameters. A comparison between the transmittance obtained by simple Beer’s law and Monte Carlo simulation reveals that the transmittance of underwater link may be severely underestimated in the previous underwater CVQKD research. The effect of the receiver aperture and field of view (FOV) on detection efficiency under different water types is further evaluated based on Monte Carlo. Simulation results show that the transmission distance of the underwater CVQKD system obtained by Monte Carlo simulation in pure sea water, clear ocean water and coastal ocean water is larger than that obtained by Beer’s law, while the key rate of the system in all types of water is smaller than that obtained by Beer’s law because the size and FOV of the receiver aperture are taken into account. By considering the practical system parameters, this paper establishes a comprehensive model for evaluating the security of underwater CVQKD systems with different system configurations.
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.
Quantum key distribution with continuous-variable (CVQKD) provides an alternative way for the security improvement of underwater optical communication, but facing into the awkward situation of short distance. For this reason, here we exploit photon addition operation at the emitter into enhancing the performance of underwater CVQKD. Based on numerical simulation, it is shown that applying photon-addition non-Gaussian operation between entangled resource and the sender can further enhance both the secure key rate and the transmission distance, compared to apply photon subtraction operation between entangled resource and the receiver. In addition, the influence of seawater quality factors in underwater CVQKD system is also considered, so as to provide technical support for underwater safety communication.
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.