  Quantum sensing employs quantum resources of a sensor to attain a smaller
estimation error of physical quantities than the limit constrained by classical
physics. To measure a quantum reservoir, which is significant in decoherence
control, a nonunitray-encoding sensing scheme becomes necessary. However,
previous studies showed that the reservoir-induced degradation to quantum
resources of the sensor makes the errors divergent with the increase of
encoding time. We here propose a scheme to use $N$ two-level systems as the
sensor to measure a quantum reservoir. A threshold, above which the
shot-noise-limited estimation error saturates or even persistently decreases
with the encoding time, is uncovered. Our analysis reveals that it is due to
the formation of a bound state of the total sensor-reservoir system. Solving
the outstanding error-divergency problem in previous studies, our result
supplies an insightful guideline in realizing a sensitive measurement of
quantum reservoirs.
