  The two-way quantum time transfer method has been proposed and experimentally
demonstrated for its potential enhancements in precision and better guarantee
of security. To further testify its advantage in practical applications, the
applicable direct transmission distance as well as the achievable
synchronization precision between independent time scales is of great interest.
In this paper, an experiment on two-way quantum time transfer has been carried
out over a 50 km long fiber link. With the common clock reference, a short-term
stability of 2.6 ps at an averaging time of 7 s and a long-term stability of
54.6 fs at 57300 s were obtained. With independent clock references, assisted
by microwave frequency transfer technology, the achieved synchronization showed
almost equal performance and reached a stability of 89.5 fs at 57300 s.
Furthermore, the spectral consistency of the utilized entangled photon pair
sources has been studied concerning its effect on the transfer accuracy and
long-term stability. The results obtained have promised a bright future of the
two-way quantum time transfer for realizing high-precision time synchronization
on metropolitan area fiber links.
