Synchronization and estimation of gravity-induced time difference for quantum clocks

TL;DR

This paper investigates how gravitational interactions between quantum clocks with different masses and energy gaps affect their synchronization and the precision of time difference estimation, highlighting the role of entanglement and quantum metrology.

Contribution

It introduces a new scenario for gravity-induced time differences in quantum clocks and analyzes how gravitational effects influence synchronization stability and measurement precision.

Findings

Synchronization precision depends on energy gaps of clocks.

Quantum Fisher information is highly sensitive to clock separation.

Quantum metrology improvements indicate entanglement generation.

Abstract

It has recently been reported [\textit{PNAS} \textbf{114}, 2303 (2017)] that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here we study an alternative scenario: the clocks have different masses and energy gaps, which would produce time difference via gravitational interaction. The proposal of quantum clock synchronization for the gravity-induced time difference is discussed. We illustrate how the stability of measurement probability in the quantum clock synchronization proposal is influenced by the gravitational interaction induced by the clock 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. We also present the quantum enhanced estimation of time difference and find that the quantum Fisher information is very sensitive to the distance between the clocks.