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A satellite-based scheme to perform clock synchronization between groundstations spread across the globe using quantum resources was proposed in [Phys.Rev. A 107, 022615 (2023)], based on the quantum clock synchronization (QCS)protocol developed in [Proc. SPIE 10547 (2018)]. Such a scheme could achievesynchronization up to the picosecond level over distances of thousands ofkilometers. Nonetheless, the implementation of this QCS protocol is yet to bedemonstrated experimentally in situations where the satellite velocities cannotbe neglected, as is the case in many realistic scenarios. In this work, wedevelop analytical and numerical tools to study the effect of the relativevelocity between the satellite and ground stations on the success of the QCSprotocol. We conclude that the protocol can still run successfully if the dataacquisition window is chosen appropriately. As a demonstration, we simulate thesynchronization outcomes for cities across the continental United States usinga single satellite in a LEO orbit, low-cost entanglement sources, portableatomic clocks, and avalanche detectors. We conclude that, after including theeffect of relative motion, sub-nanosecond to picosecond level precision canstill be achieved over distance scales of $\approx 4000$ kms. Such highprecision synchronization is currently not achievable over long distances($\gtrsim 100 km$) with standard classical techniques including the GPS. Thesimulation tools developed in this work are in principle applicable to othermeans of synchronizing clocks using entangled photons, which are expected toform the basis of future quantum networks like the Quantum Internet,distributed quantum sensing and Quantum GPS.

Synchronizing clocks via satellites using entangled photons: Effect of relative velocity on precision