  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.
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
implementation complexity which can seamlessly work on diverse transmission
lines.
