Quantum two-way time transfer with different wavelengths

Quantum networking, distributed quantum sensing and computing, financial markets, and position navigation and timing of satellites, require high precision clock synchronization. Existing quantum two-way time transfer protocols rely on identical wavelengths at each location. In this letter we derive and experimentally validate a heterogeneous wavelength quantum two-way time transfer protocol that eliminates the need for matched entangled-photon sources. The difference in propagation time is explicitly accounted for by incorporating the group refractive index to the calculations. Using a custom-built spontaneous parametric down-conversion photon-pair source, we separate signal and idler with wavelength division multiplexing, while maintaining strong frequency anti-correlation between signal and idler. We show that the dispersion effects on the second-order correlation function can be removed with the addition of dispersion compensation fiber. We performed quantum time transfer between two independent atomic clocks separated by a 15 km fiber spool with a time deviation of 658 fs at 0.2 s averaging time and 3.9 ps at 1 s averaging time. These results demonstrate a pathway for high precision time transfer in heterogeneous networks.