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Quantum metrology utilizes quantum effects to reach higher precisionmeasurements of physical quantities compared with their classical counterparts.However the ubiquitous decoherence obstructs its application. Recently,non-Markovian effects are shown to be effective in performing quantum opticalmetrology under locally dissipative environments\cite{PhysRevLett.123.040402}.However, the mechanism is still rather hazy. Here, we uncover the reason whyforming a bound state can protect the quantumness against a dissipative ambientvia the quantum Fisher information of entangled coherent states. An exactanalytical expression of the quantum Fisher information in thelong-encoding-time condition is derived, which reveals that the dynamics ofprecision can asymptotically reach the ideal-case-promised one easily when theaverage photon number is small. Meanwhile, the scaling exhibits a transitionfrom the weak Heisenberg limit to the sub-classical limit with the increase ofaverage photon number. Our work provides a recipe to realize ultrasensitivemeasurements in the presence of noise by utilizing non-Markovian effects.

Non-Markovian effect on quantum optical metrology under dissipative environment