Criterion for remote clock synchronization with Heisenberg-scaling accuracy
Yong-Liang Zhang, Yu-Ran Zhang, Liang-Zhu Mu, Heng Fan · Physical Review A · 2013
We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $\ensuremath{\sigma}$. If the measurement result of the experiment is clearly a nonzero value, the time difference between two clocks is smaller than $\ensuremath{\sigma}$; otherwise, the difference is beyond $\ensuremath{\sigma}$. Upon sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgment can be enhanced to $\ensuremath{\sigma}\ensuremath{\sim}\ensuremath{\pi}/[\ensuremath{\omega}(N+1)]$. This criterion is consistent with Heisenberg scaling, which can be considered as the beating standard quantum limit; moreover, the unbiased estimation condition is not necessary. In particular, we demonstrate that this scheme is still feasible when suffering the loss of qubits.