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.
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