Conventional strategies of quantum metrology are built upon POVMs, thereby possessing several general features, including the demolition of the state to be measured, the need of performing a number of measurements, and the degradation of performance under decoherence and dissipation. Here, we propose an innovative measurement scheme, called dissipative adiabatic measurements (DAMs), based on which, we further develop an approach to estimation of parameters characterizing dissipative processes. Unlike a POVM, whose outcome is one of the eigenvalues of an observable, a DAM yields the expectation value of the observable as its outcome, without collapsing the state to be measured. By virtue of the very nature of DAMs, our approach is capable of solving the estimation problem in a state-protective fashion with only $M$ measurements, where $M$ is the number of parameters to be estimated. More importantly, contrary to the common wisdom, it embraces decoherence and dissipation as beneficial effects and offers a Heisenberg-like scaling of precision, thus outperforming conventional strategies. Our DAM-based approach is direct, efficient, and expected to be immensely useful in the context of dissipative quantum information processing.
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