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

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.