Criterion on remote clocks synchronization within a Heisenberg scaling accuracy

We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $sigma$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $sigma$; otherwise the difference is beyond $sigma$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $sigmasim{pi}/{(omega(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.