A major outstanding problem for many quantum clock synchronization protocolsis the hidden assumption of the availability of synchronized clocks within theprotocol. In general, quantum operations between two parties do not haveconsistent phase definitions of quantum states, which introduce an unknownsystematic phase error. We show that despite prior arguments to the contrary,it is possible to remove this unknown phase via entanglement purification. Thiscloses the loophole for entanglement based quantum clock synchronizationprotocols, which are most compatible with current photon based long-distanceentanglement distribution schemes. Starting with noisy Bell pairs, we show thatthe scheme produces a singlet state for any combination of (i) differing basisconventions for Alice and Bob; (ii) an overall time offset in the execution ofthe purification algorithm; and (iii) the presence of a noisy channel. Errorestimates reveal that better performance than existing classical Einsteinsynchronization protocols should be achievable using current technology.
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