Quantum clock synchronization under decoherence effect

In this paper, we investigate the synchronization of two quantum clocks using entangled qubits, and examine how environmental noise affects the system's phase through decoherence theory. We demonstrate that, under certain conditions, the error in the final result of clock synchronization can be lower than that of current classical and quantum methods. Finally, we model the environment appropriately and apply an error correction method that takes into account the mean of the outcome over time, thus rendering the error of this method negligible.