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Journal of Physics A Mathematical and Theoretical

Phase compensation of a continuous-variable quantum key distribution via temporal convolutional neural network

Wenqi Jiang, Zhiyue Zuo, Gaofeng Luo, Hang Zhang, Ying Guo

Published Mar 8, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8121/ad31fe

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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.
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.
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.
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.
The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack.
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.
Local local oscillator (LLO) continuous-variable quantum key distribution (CVQKD) schemes have been extensively studied for their enhanced security and simplified system implementation. However, such schemes typically require numerous pilot signals to compensate for phase drift caused by two independent lasers, which significantly increases system overhead and limits the achievable secret key rate. In this work, we propose an enhanced-rate CVQKD scheme, which aims to enhance the secret key rate by achieving high-accuracy phase compensation based on a particle filter (PF) algorithm under low system overhead. Specifically, to counter the loss in phase estimation accuracy due to the reduced number of pilot signals, we introduce a PF-based carrier phase recovery algorithm, complemented by an exponentially weighted phase prediction method to improve phase estimation accuracy. This approach effectively suppresses excess noise under limited pilot information and improves phase compensation precision. Experimental results demonstrate that, compared to the traditional scheme with a 1:1 signal-to-pilot number ratio, our method achieves its maximum performance with a signal-to-pilot number ratio of 3:1, while maintaining phase compensation accuracy virtually unchanged, reducing system overhead by 50% and achieving a 147% improvement in the secret key rate, reaching 235 kbps in a 30 km standard fiber link.