Operation triggered quantum clock synchronization

We present a novel quantum clock synchronization(QCS) scheme of multiple parties which uses operation as the trigger to start the evolution of the initial state, where existing QCS protocols use measurement to start the evolution. Since the trigger is the unitary operation, we have protected entanglement of remote nodes, and after concentration of the qubits to the center node, general measurements of the total state is possible. We show that our protocol links the QCS problem to a multiple phase estimation problem. We use the Fisher information to give the precision of the synchronization, and explicitly show that the Heisenberg scale of synchronization is achieved in the two party case. We also show that our protocol is very efficient in synchronizing a clock to the average time of other clocks. The precision has an $O(\sqrt{d})$ advantage of the precision of the average time's estimation over the best possible strategy using measurement triggered QCS. The precision is also Heisenberg scale.