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arXiv:quant-ph/0605013 · Laser Physics

On decoherence in quantum clock synchronization

Sergio Boixo, Carlton M. Caves, Animesh Datta, Anil Shaji

Published Oct 30, 2006• 19 citations
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Abstract

We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.

DOI
10.1134/s1054660x06110065

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We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.
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.
Recently a protocol for Quantum Clock Synchronization (QCS) of remote clocks using quantum entanglement was proposed by Jozsa et al. This method has the goal of eliminating the random noise present in classical synchronization techniques. However, as stated QCS depends on the two members of each entangled pair undergoing the same unitary evolution even while being transported to different locations. This is essentially equivalent to a perfect Eddington Slow Clock Transfer protocol and thus, not an improvement over classical techniques. We will discuss this and suggest ways in which QCS may still be used.
Abstract In this paper, we study a quantum clock synchronization for a three observer locating system, using entangled qubits and discuss the effect of the environmental noise on the phase of the system using decoherence theory. We will show that the error on the final result of the clock synchronization can be less than the current classical synchronizations, under suitable circumstances. Finally, with an appropriate modelling of the environment we can correct the error of the synchronization for a more accurate locating.
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 A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of a common phase reference between the parties to be synchronized. In general, the definition of the quantum states between two parties do not have consistent phase definitions, which can lead to an unknown systematic error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology.
Synchronizing clocks using quantum entanglement works on the principle that two clocks Alice and Bob share between them a singlet state which is a stationary state that is immune to evolution under bare atomic Hamiltonian. A major obstacle to its realization is the hidden assumption of a common phase reference between the clocks. Without hidden assumption, a clock state of Alice or Bob is not a uniquely defined quantum state because the phase of the state is arbitrary. This results in an unknown relative phase in a two-particle entangled state defined by the clocks. We show that using entanglement purification, an entanglement-based clock synchronization is achieved despite earlier results showing the contrary. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium.