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Optics Express

Deep learning-based defense against phase-injection attacks in pilot-multiplexed continuous-variable quantum key distribution

Tao Shen, Jiayu Ma, Xiangyu Wang

Published Apr 7, 2026• 0 citations
Publisher

Abstract

Accurate phase estimation is essential for continuous-variable quantum key distribution (CV-QKD), particularly in local local oscillator systems that rely on publicly multiplexed pilot tones for phase recovery. While efficient, pilot-based schemes render the phase-tracking process susceptible to adversarial manipulation, allowing an eavesdropper to systematically bias the phase estimation and consequently compromise system security, without inducing noticeable changes in the estimated channel parameters. In this work, we demonstrate a phase-injection attack that introduces subtle non-Gaussian perturbations into the pilot tones, leading to systematic phase estimation errors under conventional algorithms. To mitigate this vulnerability, we propose a Gated-Robust Long Short-Term Memory (GR-LSTM)-based phase estimation scheme. During training, the network incorporates both legitimate phase and synthetically generated attack-induced perturbations, enabling it to learn robust temporal representations that attenuate attack-related anomalies while preserving the underlying phase evolution. Numerical simulations and a 20 km fiber experiment confirm that the proposed GR-LSTM effectively restores robust phase estimation under attack. As a result, the average secret key rate increases from 1.143 Mbps with a standard LSTM to 1.588 Mbps, corresponding to a 38.9% improvement, demonstrating a practical security enhancement for pilot-multiplexed CV-QKD systems.

DOI
10.1364/oe.590610

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Accurate phase estimation is essential for continuous-variable quantum key distribution (CV-QKD), particularly in local local oscillator systems that rely on publicly multiplexed pilot tones for phase recovery. While efficient, pilot-based schemes render the phase-tracking process susceptible to adversarial manipulation, allowing an eavesdropper to systematically bias the phase estimation and consequently compromise system security, without inducing noticeable changes in the estimated channel parameters. In this work, we demonstrate a phase-injection attack that introduces subtle non-Gaussian perturbations into the pilot tones, leading to systematic phase estimation errors under conventional algorithms. To mitigate this vulnerability, we propose a Gated-Robust Long Short-Term Memory (GR-LSTM)-based phase estimation scheme. During training, the network incorporates both legitimate phase and synthetically generated attack-induced perturbations, enabling it to learn robust temporal representations that attenuate attack-related anomalies while preserving the underlying phase evolution. Numerical simulations and a 20 km fiber experiment confirm that the proposed GR-LSTM effectively restores robust phase estimation under attack. As a result, the average secret key rate increases from 1.143 Mbps with a standard LSTM to 1.588 Mbps, corresponding to a 38.9% improvement, demonstrating a practical security enhancement for pilot-multiplexed CV-QKD systems.
Local local oscillator (LLO) continuous-variable quantum key distribution (CVQKD) systems have gained prominence due to their security advantages with LO generated locally. However, the nonsynchronization of two lasers leads to phase drift, a detrimental phenomenon that restricts excess noise suppression. Prevailing solutions, such as pilot-multiplexing schemes, offer better recovery results than pilot-sequential schemes, but at the expense of increased system complexity and demanding technical requirements. In this work, we introduce an innovative carrier-recovery strategy employing the long-short-term memory (LSTM) neural network, aiming to optimize the recovery performance in the simple self-referenced CVQKD systems with the pilot-sequential scheme. Through temporal modeling, the LSTM network proficiently predicts and compensates for the rapid phase drifts. Experimental validations conducted in both fiber and free-space channels underscore the effectiveness of our method for carrier recovery. In practical CVQKD experiments, our LSTM-based approach yields a near 50% reduction in excess noise, leading to a significant increase in secret key rates when compared with the traditional pilot-sequential method. The simplicity of hardware and operation positions our scheme as a superior alternative for current mainstream pilot-multiplexing CVQKD systems, particularly appealing for on-chip implementation and satellite-to-ground quantum communication applications.
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.
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.
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.
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.
The performance of local local oscillator-based continuous-variable quantum key distribution (LLO-CVQKD) systems is critically limited by phase recovery accuracy. To address the phase mismatch between independently operated lasers at the transmitter and receiver, this work proposes a multi-pilot scheme integrated with advanced digital filtering for optimized phase estimation. Through systematic comparisons of the rectangular filter, Savitzky-Golay filter, and Wiener filter, experimental results confirm that Wiener filtering has superior noise suppression capabilities based on multiple frequency pilot-tones. Implemented under the Gaussian-modulated coherent state (GMCS) protocol, our findings reveal that dual-pilot, four-pilot, and eight-pilot configurations all enhance phase recovery precision compared to single-pilot approaches, with the dual-pilot scheme achieving optimal balance between system complexity and performance. In a 20 km fiber link with a 1 GHz system repetition rate and a 2.83 SNU modulation variance, the dual-pilot Wiener-filtered configuration achieves an asymptotic secret key rate of almost 80 Mbps, establishing an innovative approach for practical LLO-CVQKD phase recovery.