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arXiv:1709.08423 · npj Quantum Information

Remote quantum clock synchronization without synchronized clocks

Ebubechukwu O. Ilo-Okeke, Louis Tessler, Jonathan P. Dowling, Tim Byrnes

Published Aug 9, 2018• 78 citations
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Abstract

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.

DOI
10.1038/s41534-018-0090-2

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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.
Recent work has raised the possibility that quantum-information-theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties [R. Jozsa et al., Phys. Rev. Lett. 858585 2010 (2000)]. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state, which then needs to be purified asynchronously. We present a relativistic analysis of the QCS protocol that shows that asynchronous entanglement purification is not possible, and, therefore, the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum-information theory, which may lead to a complete, working QCS protocol.
We investigate methods to broadcast timing information from a central clock to all other clocks by the use of multipartite entanglement. This task is a necessary step in establishing a coordinated universal time, currently performed using classical synchronization methods. Using an entanglement-based method has the advantage that the timing results are independent of the intervening medium. We generalize existing bipartite quantum clock synchronization methods and take special care to address issues of different phase conventions being adopted at each node (the ``Preskill phase problem''). Using supersinglet purification, we show that this allows for a scalable method with a time signal that is a constant with respect to the number of nodes.
The ability to synchronize remote clocks plays an increasingly important role in our infrastructure, from maintaining coherence in the electrical grid to allowing precise positioning and navigation for civilian and military applications. However, many of the techniques to establish and maintain this time synchronization have been shown to be susceptible to interference by malicious parties. Here we propose a protocol that builds on techniques from quantum communication to provide a verified and secure time synchronization protocol. In contrast with classical protocols aimed at increasing the security of time distribution, we need not make any assumptions about the distance or propagation times between the clocks. In order to compromise the security of the protocol, an adversary must be able to perform quantum non-demolition measurements of the presence of a singe photon with high probability. The requirement of such quantum measurements raises a serious technological barrier for any would-be adversary