We examine a system in which an impurity qubit is immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate whose collective excitations act as a dephasing reservoir for the qubit. The relative dipole-dipole interaction strength is estimated by the probe qubit dephasing. The ultimate precision of this estimation is quantified by the quantum Fisher information (QFI), which can be obtained by means of measuring quantum coherence of the probe qubit. Our findings indicate that, in the interval where roton excitations appear, the QFI oscillates periodically with the evolution time $t$, and the amplitude of these oscillations increases alongside the extension of $t$. Moreover, we analytically determine that the envelope curve formed by the local maximum points satisfies the functional relationship $At+B{t}^{1/2}+C$ during long-term encoding scenarios, where $A, B$, and $C$ are positive numbers. It is revealed that the highly non-Markovian effects caused by the roton softening of the excitation spectrum allow long evolution time to serve as a resource for enhancing sensing precision. We also study the effects of the reservoir's temperature on the dynamics of the QFI. It is found that lower temperatures have virtually no effect, while higher temperatures can accelerate the growth rate of the QFI with evolution time, reflecting that thermal noise can be used to enhance the quantum advantage in quantum sensing. Our work provides a new pathway for enhancing the sensing precision of dephasing qubits.

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• Quantum parameter estimation