Remote quantum clock synchronization without synchronized clocks

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.Quantum protocols: Set the time with purified entanglementQuantum mechanics can be used to synchronise the clocks of two distant parties by using the non-local properties of entanglement. It was shown in 2000 that, if two parties share entangled qubit pairs, performing coordinated quantum operations allows them to detect systematic errors in their measurements of time. Unfortunately, performing the correct manipulations already implicitly requires some degree of synchronisation. Ebubechukwu Ilo-Okeke and colleagues from New York University Shanghai and Louisiana State University show that this can be resolved using quantum purification, which concentrates the entanglement from many qubits into states with higher entanglement. They demonstrate that when the parties are out of sync the purification generates states that account for the discrepancy and then can be used for synchronisation. If fully developed, the quantum synchronization scheme could outperform existing classical methods.