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It has recently been reported that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here, an alternative scenario is studied: The clocks have different masses and energy gaps, which would produce time differences via gravitational interaction. The proposal of quantum clock synchronization (QCS) for the gravity‐induced time difference is discussed. It is illustrated how the stability of measurement probability in the QCS proposal is influenced by the gravitational interaction induced by the clocks themselves. It is found that the precision of clock synchronization depends on the energy gaps of the clocks and the improvement of precision in quantum metrology is in fact an indicator of entanglement generation. The quantum enhanced estimation of time difference is also presented and it is found that the quantum Fisher information is very sensitive to the distance between the clocks.

Synchronization and Estimation of Gravity‐Induced Time Difference for Quantum Clocks