  High-precision frequency alignment with classical communication channels is
difficult due to noise, propagation delays, and signal degradation. Current
optical methods, commonly involving frequency combs, are capable of
synchronising clocks with exceptional precision up to the region of a part in
10e20. Alternatively, wireless methods see use where this is not practical,
with achievable precision within the nanosecond region. This leaves few options
for achieving high-precision clock synchronisation without requiring
specialised equipment, a fibre connection, or a line of sight communication
channel. Here we present a novel approach combining quantum state
reconstruction with feedback controls to stabilize the frequency of two atomic
clocks separated by a 900 MHz free space radio link. Quantum state
reconstruction enables tracking of phase and frequency fluctuations during
transmission. We see that a part in 10e16 precision in frequency alignment of
the clocks can be achieved using commonly-available radio equipment, allowing
precise timekeeping and synchronization over long distances provided a radio
communications channel can be established, with potential applications in a
wide variety of timekeeping applications.
