Quantum Clock Synchronization in Noisy Channel

Previous researches show that the quantum clock synchronization can achieve a high accuracy in noise-free channel. However, there is much noise in actual channel. The noise may introduce some errors during synchronization. The paper study the accuracy in two noisy channels: Bit flip channel and Phase flip channel. We find the pollution channel may usually degrade time accuracy. And the accuracy of Phase flip may be worse than accuracy of Bit flip. In some pollution case, quantum clock synchronization does not provide any valuable time information.