  Preserving the precision of the parameter of interest in the presence of
environmental decoherence is an important yet challenging task in dissipative
quantum sensing. In this work, we study quantum metrology when the decoherence
effect is unraveled by a set of quantum measurements,dubbed quantum measurement
encoding. In our case, the estimation parameter is encoded into a quantum state
through a quantum measurement, unlike the parameter encoding through a unitary
channel in the decoherence-free case or trace-preserving quantum channels in
the case of decoherence. We identify conditions for a precision-preserving
measurement encoding. These conditions can be employed to transfer metrological
information from one subsystem to another through quantum measurements.
Furthermore, postselected non-Hermitian sensing can also be viewed as quantum
sensing with measurement encoding. When the precision-preserving conditions are
violated in non-Hermitian sensing, we derive a universal formula for the loss
of precision.
