Criterion on remote clocks synchronization within a Heisenberg scaling accuracy

TL;DR

This paper introduces a quantum method for assessing whether two distant clocks are synchronized within a certain accuracy, achieving Heisenberg scaling and surpassing the standard quantum limit without requiring unbiased estimation.

Contribution

The authors propose a novel quantum criterion for clock synchronization that leverages entanglement and Heisenberg scaling to improve accuracy beyond classical limits.

Findings

Achieves synchronization accuracy scaling as rac{pi}{omega(N+1)}

Utilizes bipartite maximally entangled states for enhanced precision

Does not require unbiased estimation conditions

Abstract

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 $\sigma\sim{\pi}/{(\omega(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.