Criterion on remote clocks synchronization within a Heisenberg scaling accuracy

Abstract

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

5 pages, 1 figure