  High-precision time transfer is of fundamental interest in physics and
metrology. Quantum time transfer technologies that use frequency-entangled
pulses and their coincidence detection have been proposed, offering potential
enhancements in precision and better guarantees of security. In this paper, we
describe a fiber-optic two-way quantum time transfer experiment. Using quantum
nonlocal dispersion cancellation, time transfer over a 20-km fiber link
achieves a time deviation of 922 fs over 5 s and 45 fs over 40960 s. The time
transfer accuracy as a function of fiber lengths from 15 m to 20 km is also
investigated, and an uncertainty of 2.46 ps in standard deviation is observed.
In comparison with its classical counterparts, the fiber-optic two-way quantum
time transfer setup shows appreciable improvement, and further enhancements
could be obtained by using new event timers with sub-picosecond precision and
single-photon detectors with lower timing jitter for optimized coincidence
detection. Combined with its security advantages, the femtosecond-scale two-way
quantum time transfer is expected to have numerous applications in
high-precision middle-haul synchronization systems.
