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Photonics

Phase Compensation for Continuous Variable Quantum Key Distribution Based on Convolutional Neural Network

Zhuangzhuang Xing, Xingqiao Li, Xinchao Ruan, Yong Luo, Hang Zhang

Published Jun 30, 2022• 10 citations
Publisher

Abstract

Phase drift extremely limits the secure key rate and secure transmission distance, which is non-negligible in local oscillation continuous variable quantum key distribution (LLO CV-QKD). In order to eliminate the impact caused by phase drift, we analyze the phase noise of the system and propose a phase compensation method based on convolutional neural network (CNN). Moreover, the compensation is performed on the signal according to the estimated value of phase drift before coherent detection. In numerical simulation, we compare the performance of phase compensation methods based on CNN and Kalman filter (KF), and the results show that CNN-based phase compensation has higher accuracy and stability.

DOI
10.3390/photonics9070463

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Journal of Applied Mathematics and Physics•Jan 1, 2019•1 citation
Phase drift extremely limits the secure key rate and secure transmission distance, which is non-negligible in local oscillation continuous variable quantum key distribution (LLO CV-QKD). In order to eliminate the impact caused by phase drift, we analyze the phase noise of the system and propose a phase compensation method based on convolutional neural network (CNN). Moreover, the compensation is performed on the signal according to the estimated value of phase drift before coherent detection. In numerical simulation, we compare the performance of phase compensation methods based on CNN and Kalman filter (KF), and the results show that CNN-based phase compensation has higher accuracy and stability.
Abstract Although the continuous-variable quantum key distribution (CV-QKD) protocol based on a local local oscillator (LLO) can close all the security loopholes from the transmitted local oscillator (TLO), the phase noise caused by the inaccurate phase reference information limits the performance of the protocol. To reduce the residual phase noise, in this work, we propose a phase estimation and compensation method based on the temporal convolutional neural (TCN) model, where a part of phase information obtained by measuring pilot pulses is employed as the training data and input into the TCN module. With a trained TCN module, the subsequent phase drifts can be more accurately estimated, allowing for better phase compensation and lower phase noise. Numerical analysis shows that the proposed scheme can improve the transmission distance and the secret key rate of the LLO protocol.
The value of residual phase noise, after phase compensation, is one of the key limitations of performance improvement for continuous-variable quantum key distribution using a local local oscillator (LLO CV-QKD) system, since it is the major excess noise. However, due to the nonideality of the realistic devices implemented in practice, for example, imperfect lasers, detectors, and unbalanced interferometers, the value of residual phase noise in the current system is still relatively large. Here, we develop a phase noise model to improve the phase noise tolerance of the LLO CV-QKD schemes. In our model, part of the phase-reference measurement noise associated with detection efficiency and electronic noise of Bob's detector as well as a real-time monitored phase-reference intensity at Bob's side is considered trusted because it can be locally calibrated by Bob. We show that using our phase noise model can significantly improve the secure key rate and transmission distance of the LLO CV-QKD system. We further conduct an experiment to substantiate the superiority of the phase noise model. Based on experimental data of a LLO CV-QKD system in the 25-km optical fiber channel, we demonstrate that the secure key rate under our phase noise model is approximately 40% higher than that under the conventional phase noise model.
Continuous-variable quantum key distribution (CV-QKD) holds promise for enhancing security in communication networks. However, obtaining a higher secure key rate poses challenges, particularly in reliable phase estimation. So, it is very necessary for CV-QKD implementations with independent local oscillator (LO) to employ carrier recovery along with precise phase estimation. Our methodology combines extended Kalman filters (EKF) with recurrent neural networks (RNNs) to enhance the accuracy of phase recovery for locally generated LO signals. Using numerical simulations, we evaluate the achievable secret key rates for different transmission distances and line widths. The proposed method achieves a phase error of approximately 1 × 10–4, leading to positive secure key rates for distances up to 40 km. This method of phase tracking solves the problem and is effective in real-time deployment of CV-QKD in communication networks.
The continuous-variable quantum key distribution with a local local-oscillator is extremely sensitive to the phase compensation noise caused by the inaccurate reference phase estimation. In order to overcome the influence of slow drift caused by the residual optical frequency difference, we utilize a vector Kalman filter to estimate and track the reference phase from pilots. The fast drift and slow drift are taken into account in the variation of the reference phase, so that phase estimation becomes more accurate than the conventional scalar Kalman filter. The mean square error of reference phase estimation is deduced theoretically, and the specified frame is designed to estimate the phase noise variance in real time. In simulations, the performances involving of the estimation accuracy, the actual excess noise and the secret key rate are compared between with four different phase estimation methods. The simulation results show that the vector Kalman filter is superior to the other methods, even though under a serious phase noise and a large optical frequency difference.
In continuous-variable quantum key distribution with a local local oscillator (LLO CV-QKD), the phase noise after phase compensation is mainly composed of three parts: the relative phase drift noise, the relative phase accumulated noise, and the phase-reference measurement noise. Here, we develop a practical phase noise model for LLO CV-QKD protocols, in which part of the phase-reference measurement noise that can be locally calibrated by Bob at the receiver side is considered to be trusted noise. It is reasonable to adopt this model because Bob”s apparatus is inaccessible to the eavesdropper. We show that the secret key rate and the transmission distance of the LLO CV-QKD system under the practical phase noise model is significantly improved in comparison to that under the conventional phase noise model. We show that the secret key rate is improved more than 65% and the transmission distance is increased more than 70% with some typical simulation parameters.
Continuous-variable quantum key distribution (CVQKD) with the local local oscillator (LLO) is confronted with new security problems due to the reference pulses transmitted together with quantum signals over the insecure quantum channel. In this paper, we propose a method of phase attack on reference pulses of the LLO-CVQKD with time-multiplexing. Under this phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers, and then the phase compensation error is increased. Consequently, the secret key rate is reduced due to the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, the practical security of LLO-CVQKD under phase attack is analyzed. The simulation results show that the practical security is reduced due to the phase attack, yet it is still tight when system parameters are estimated by training signals.