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arXiv:cs/0103021

Quantum Clock Synchronization with one qubit

Chris Harrelson, Iordanis Kerenidis

Published Mar 28, 2001• 2 citations
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Abstract

The clock synchronization problem is to determine the time difference T between two spatially separated parties. We improve on I. Chuang's quantum clock synchronization algorithm and show that it is possible to obtain T to n bits of accuracy while communicating only one qubit in one direction and using an O(2^n) frequency range. We also prove a quantum lower bound of Ω(2^n) for the product of the transmitted qubits and the range of frequencies, thus showing that our algorithm is optimal.

DOI
10.48550/arxiv.cs/0103021

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The clock synchronization problem is to determine the time difference T between two spatially separated parties. We improve on I. Chuang's quantum clock synchronization algorithm and show that it is possible to obtain T to n bits of accuracy while communicating only one qubit in one direction and using an O(2^n) frequency range. We also prove a quantum lower bound of Ω(2^n) for the product of the transmitted qubits and the range of frequencies, thus showing that our algorithm is optimal.
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.
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.
The quantum clock synchronization (QCS) is to measure the time difference among the spatially separated clocks with the principle of quantum mechanics. The first QCS algorithm proposed by Chuang and Jozsa is merely based on two parties, which is further extended and generalized to the multiparty situation by Krco and Paul. They present a multiparty QCS protocol based upon W states that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Shortly afterwards, Ben-Av and Exman came up with an optimized multiparty QCS using Z state. In this work, we firstly report an implementation of Krco and Ben-AV multiparty QCS algorithm using a four-qubit Nuclear Magnetic Resonance (NMR). The experimental results show a great agreement with the theory and also prove Ben-AV multiparty QCS algorithm more accurate than Krco.
A multiparty protocol for distributed quantum clock synchronization has been claimed to provide universal limits on the clock accuracy, viz., that accuracy monotonically decreases with the number nnn of party members. But this is only true for synchronization when one limits oneself to WWW states. This work shows that the usage of Z (Symmetric Dicke) states, a generalization of WWW states, results in improved accuracy, having a maximum when $\ensuremath{\lfloor}n/2\ensuremath{\rfloor}$ of its members have their qubits with a $|1\ensuremath{\rangle}$ eigenstate.
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 2NNN-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.