Enhancing noise suppression of phase estimation in continuous-variable quantum key distribution with discrete modulation

Accurately estimating phase is crucial in continuous-variable quantum key distribution systems, directly impacting the final secret key rate. In previous systems that utilize the local local oscillator, phase estimation is closely tied to the amplitude and signal-to-noise ratio (SNR) of the pilot signal. As SNR decreases, so does the accuracy of phase estimation, leading to increased excess noise and a potential loss of the system's secret key rate. The SNR of the pilot signal is constrained by the optical source power, which tends to approach 0 dB, particularly over long distances. Enhancing the accuracy of phase estimation under conditions of low SNR for pilot signals is highly challenging, especially in long-distance quantum key distribution. Our paper proposes two digital filter methods: the unscented Kalman filtering (UKF) and the Savitzky-Golay filtering (SGF) for phase estimation, which effectively mitigates the effects of additive noise. The approach applies to digital systems and therefore holds particular advantages in systems based on discrete-modulation (DM) protocols. Through simulations and practical implementation based on DM protocols, we find that the digital filter scheme is capable of accurately estimating phase, especially in scenarios with low SNR of the pilot signal. The conventional method fails to achieve an effective secret key rate, whereas the digital-filter-based scheme achieves a secret key rate of almost 30 kbps over a 20 km fiber link with a repetition frequency of 5 MHz under conditions where the SNR of the pilot signal is around 0 dB.