Single-photon time-of-flight measurements for benchmarking time transfer in quantum networks

We propose a single-photon time-of-flight (ToF) measurement method to benchmark fiber-path delay estimation in optical two-way time and frequency transfer (OTWTFT) protocols. The single-photon ToF measurement yields uncertainties better than 2 ps (0.5 mm fiber-path-length uncertainty) at 1 s integration times for a deployed 120 km (loopback) fiber. Differences between the ToF and the roundtrip time measurements from a White Rabbit precision time protocol appear to correlate with the clock phase error between two White Rabbit switches. The results suggest that augmenting single-photon ToF measurements with existing OTWTFT protocols could enhance the precision to sub-10-ps levels at metropolitan distances. Such a level of precision will be critical for synchronization in quantum networks.