1. Introduction . Since the beginning of the 21st century, clock synchronization schemes based on quantum entanglement and compressed states have been widely investigated because of their improvement in accuracy and potential applications in secure clock transfer. In terms of clock accuracy, the number-squeezed states $\left n\right \rangle$ in the $m$ -fold entangled state can enhance the accuracy limit by $\sqrt {mn}$ times [ 1 ]. For the security of clock transfer, the non-local...