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

TL;DR

This paper investigates how satellite velocity affects quantum clock synchronization using entangled photons, demonstrating that high-precision synchronization remains feasible with proper data acquisition timing.

Contribution

It develops analytical and numerical methods to assess the impact of relative motion on quantum clock synchronization protocols and demonstrates their effectiveness through realistic simulations.

Findings

Successful synchronization at sub-nanosecond to picosecond levels over 4000 km.

Protocol remains effective with appropriate data window adjustments.

High-precision quantum synchronization surpasses classical GPS capabilities.

Abstract

A satellite-based scheme to perform clock synchronization between ground stations 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 achieve synchronization up to the picosecond level over distances of thousands of kilometers. Nonetheless, the implementation of this QCS protocol is yet to be demonstrated experimentally in situations where the satellite velocities cannot be neglected, as is the case in many realistic scenarios. In this work, we develop analytical and numerical tools to study the effect of the relative velocity between the satellite and ground stations on the success of the QCS protocol. We conclude that the protocol can still run successfully if the data acquisition window is chosen appropriately. As a demonstration, we simulate the synchronization outcomes for cities across the continental United States using a single satellite in a LEO orbit, low-cost entanglement sources, portable atomic clocks, and avalanche detectors. We conclude that, after including the effect of relative motion, sub-nanosecond to picosecond level precision can still be achieved over distance scales of $\approx 4000$ kms. Such high precision synchronization is currently not achievable over long distances ($\gtrsim 100 km$) with standard classical techniques including the GPS. The simulation tools developed in this work are in principle applicable to other means of synchronizing clocks using entangled photons, which are expected to form the basis of future quantum networks like the Quantum Internet, distributed quantum sensing and Quantum GPS.