The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the frequency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we explore the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method and a previously demonstrated machine learning method. Experimental results obtained over a 20-km fibre-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. This may enable CV-QKD systems with low hardware implementation complexity which can seamlessly work on diverse transmission lines.

连续变量量子密钥分配（CV-QKD）系统的秘密密钥速率受到过多噪声的限制。使用参考信号或导频信号以及独立的本机振荡器实现的所有现代CV-QKD系统的典型关键问题是控制由发射器和接收器产生的频率和相位噪声产生的多余噪声。因此，准确的相位估计和补偿（所谓的载波恢复）是CV-QKD的关键子系统。在这里，我们探索基于贝叶斯推断的机器学习框架的实现，即无味卡尔曼滤波器（UKF），用于估计相位噪声，并将其与标准参考方法和先前证明的机器学习方法进行比较。在20公里的光纤链路上获得的实验结果表明，即使在低导频功率下，UKF也可以确保非常低的过量噪声。在较大的导频信噪比范围内，测量结果显示出在多余噪声中的低方差和高稳定性。这可以使硬件实现复杂度较低的CV-QKD系统能够在各种传输线上无缝运行。