  Quantum sensing explores protocols using the quantum resource of sensors to
achieve highly sensitive measurement of physical quantities. The conventional
schemes generally use unitary dynamics to encode quantities into sensor states.
In order to measure the spectral density of a quantum reservoir, which plays a
vital role in controlling the reservoir-caused decoherence to microscopic
systems, we propose a nonunitary-encoding optical sensing scheme. Although the
nonunitary dynamics for encoding in turn degrades the quantum resource, we
surprisingly find a mechanism to make the encoding time a resource to improve
the precision and to make the squeezing of the sensor a resource to surpass the
shot-noise limit. Our result shows that it is due to the formation of a
sensor-reservoir bound state. Enriching the family of quantum sensing, our
scheme gives an efficient way to measure the quantum reservoir and might supply
an insightful support to decoherence control.
