Quantum metrology explores quantum features to ameliorate resolution, precision, and sensitivity beyond classical limits when the quantum theory determines the ultimate limit on the accuracy of any measurement. More recently, it is shown that entangled coherent states (ECSs) have the potential to perform robust sub-classical measurements considering only the case of a weak-coupling regime. In this paper, we examine the dynamics of the phase sensitivity for ECSs in the framework of the non-Markovian lossy channels and show how the non-Markovian features and reservoir parameters may be exploited for quantum-enhanced phase estimation. The influences of memory effects and the Ohmic reservoir with Lorentz–Drude regularization are examined under the following conditions: , , or , where is the field mode frequency of interest and is the cutoff frequency of the Ohmic reservoir. In shape contract with results obtained in the presence of Markovian lossy, we obtain that the memory effects lead to an enhanced phase estimation while the ratio provides a way to control and improve the precision during the time evolution. We show that the smallest variance in the phase parameter highly depends on the combination of the ration and non-Markovian effects.
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