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arXiv:1303.3437 · Physical Review A

Criterion for remote clock synchronization with Heisenberg-scaling accuracy

Yong-Liang Zhang, Yu-Ran Zhang, Liang-Zhu Mu, Heng Fan

Published Nov 13, 2013• 22 citations

Abstract

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.

DOI: 10.1103/physreva.88.052314

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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.

We introduce methods for clock synchronization that make use of the adiabatic exchange of nondegenerate two-level quantum systems: ticking qubits. Schemes involving the exchange of

N

independent qubits with frequency $\ensuremath{\omega}$ give a synchronization accuracy that scales as ${(\ensuremath{\omega}\sqrt{N})}^{\ensuremath{-}1}$---i.e., as the standard quantum limit. We introduce a protocol that makes use of

{N}_{c}

coherent exchanges of a single qubit at frequency $\ensuremath{\omega}$, leading to an accuracy that scales as ${(\ensuremath{\omega}{N}_{c})}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{N}_{c}$. This protocol beats the standard quantum limit without the use of entanglement, and we argue that this scaling is the fundamental limit for clock synchronization allowed by quantum mechanics. We analyze the performance of these protocols when used with a lossy channel.

Clock synchronization is a well-studied problem with many practical and scientific applications. We propose an arbitrary accuracy iterative quantum algorithm for distributed clock synchronization using only three qubits. The n bits of the time difference Δ between two spatially separated clocks can be deterministically extracted by communicating only O ( n ) messages and executing the quantum iteration process n times based on the classical feedback and measurement operations. Finally, we also give the algorithm using only two qubits and discuss the success probability of the algorithm.

Clock synchronization is a well-studied problem with many practical and scientific applications.We propose an arbitrary accuracy iterative quantum algorithm for distributed clock synchronization using only three qubits.The n bits of the time difference between two spatially separated clocks can be deterministically extracted by communicating only O(n) messages and executing the quantum iteration process n times based on the classical feedback and measurement operations.Finally,we also give the algorithm using only two qubits and discuss the success probability of the algorithm.

This study presents a clock synchronization method based on quantum entanglement which is simple and reliable and more efficient. The clock synchronization method based on quantum entanglement scheme can greatly improve the accuracy and precision of measurement. More importantly, the proposed method avoids synchronization error caused by traditional method due to the asymmetry of two-way delay. The probability of measuring the quantum state oscillates in cosine or sine fashion with propagation delay. The final experimental and simulation results are basically consistent with the theoretical results. The clock synchronization method based on quantum entanglement scheme can greatly imrprove the accuracy and precision of measurement.