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arXiv:1105.0186 · Physical Review A

Optimized multiparty quantum clock synchronization

Radel Ben-Av, Iaakov Exman

Published Jul 5, 2011• 30 citations
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Abstract

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 $n$ of party members. But this is only true for synchronization when one limits oneself to $W$ states. This work shows that the usage of Z (Symmetric Dicke) states, a generalization of $W$ 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.

DOI
10.1103/physreva.84.014301

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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⌊n/2\ensuremath⌋\ensuremath{\lfloor}n/2\ensuremath{\rfloor}\ensuremath⌊n/2\ensuremath⌋ of its members have their qubits with a ∣1\ensuremath⟩|1\ensuremath{\rangle}∣1\ensuremath⟩ eigenstate.
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.
We propose a multiparty quantum clock synchronization protocol that makes optimal use of the maximal multipartite entanglement of GHZ-type states. To realize the protocol, different versions of maximally entangled eigenstates of collective energy are generated by local transformations that distinguish among different groupings of the parties. The maximal sensitivity of the entangled states to time differences between the local clocks can then be accessed if all parties share the results of their local time-dependent measurements. The efficiency of the protocol is evaluated in terms of the statistical errors in the estimation of time differences and the performance of the protocol is compared to alternative protocols proposed previously.
Abstract This paper investigates multipartite quantum clock synchronization (QCS) procedures using a new class of quantum states called collective symmetric (CS) states, which generalize Dicke and N00N-type states. Among all the QCS techniques proposed in the literature, the focus here is on procedures relying on local operations and classical communication (LOCC). Two synchronization scenarios that are particularly useful for quantum networks are considered: (i) pair synchronization where multiple arbitrarily chosen disjoint pairs of nodes aim to align their clocks, and (ii) network synchronization where all nodes aim to synchronize their clocks to a common average time. First, the paper discusses the use of CS states in QCS procedures previously proposed in the literature for both scenarios. Second, possible limitations of the QCS procedures are considered in terms of insufficient robustness and estimation ambiguity. Third, a new procedure, referred to as efficient synchronization procedure (ESP), is designed for each of the two synchronization scenarios. The ESP is shown to address the aforementioned limitations and to outperform the state-of-the-art LOCC-based multipartite QCS procedures in terms of synchronization precision.
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 NNN 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 Nc{N}_{c}Nc​ 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.