  Non-conventional receivers for phase-coherent states based on non-Gaussian
measurements such as photon counting surpass the sensitivity limits of
shot-noise-limited coherent receivers, the quantum noise limit (QNL). These
non-Gaussian receivers can have a significant impact in future coherent
communication technologies. However, random phase changes in realistic
communication channels, such as optical fibers, present serious challenges for
extracting the information encoded in coherent states. While there are methods
for correcting random phase noise with conventional heterodyne detection,
phase-tracking for non-Gaussian receivers surpassing the QNL is still an open
problem. Here we demonstrate phase tracking for non-Gaussian receivers to
correct for time-varying phase noise while allowing for decoding beyond the
QNL. The phase-tracking method performs real-time parameter estimation and
correction of phase drifts using the data from the non-Gaussian discrimination
measurement, without relying on phase reference pilot fields. This method
enables non-Gaussian receivers to achieve higher sensitivities and rates of
information transfer than ideal coherent receivers in realistic channels with
time-varying phase noise. This demonstration makes sub-QNL receivers a more
robust, feasible, and practical quantum technology for classical and quantum
communications.
