It is challenged only recently that the precision attainable in any measurement of a physical parameter is fundamentally limited by the quantum Cram{e}r-Rao Bound (QCRB). Here, targeting at measuring parameters in strongly dissipative systems, we propose an innovative measurement scheme called {it dissipative adiabatic measurement} and theoretically show that it can beat the QCRB. Unlike projective measurements, our measurement scheme, though consuming more time, does not collapse the measured state and, more importantly, yields the expectation value of an observable as its measurement outcome, which is directly connected to the parameter of interest. Such a direct connection {allows to extract} the value of the parameter from the measurement outcomes in a straightforward manner, with no fundamental limitation on precision in principle. Our findings not only provide a marked insight into quantum metrology but also are highly useful in dissipative quantum information processing.
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