  Continuous monitoring of driven-dissipative quantum optical systems is a
crucial element in the implementation of quantum metrology, providing essential
strategies for achieving highly precise measurements beyond the classical
limit. In this context, the relevant figure of merit is the quantum Fisher
information of the radiation field emitted by the driven-dissipative sensor.
Saturation of the corresponding precision limit as defined by the quantum
Cramer-Rao bound is typically not achieved by conventional, temporally local
continuous measurement schemes such as counting or homodyning. To address the
outstanding open challenge of efficient retrieval of the quantum Fisher
information of the emission field, we design a novel continuous measurement
strategy featuring temporally quasilocal measurement bases as captured by
matrix product states. Such measurement can be implemented effectively by
injecting the emission field of the sensor into an auxiliary open system, a
`quantum decoder' module, which `decodes' specific input matrix product states
into simple product states as its output field, and performing conventional
continuous measurement at the output. We devise a universal recipe for the
construction of the decoder by exploiting time reversal transformation of
quantum optical input-output channels, thereby establishing a universal method
to achieve the quantum Cramer-Rao precision limit for generic sensors based on
continuous measurement. As a by-product, we establish an effective formula for
the evaluation of the quantum Fisher information of the emission field of
generic driven-dissipative open sensors. We illustrate the power of our scheme
with paramagnetic open sensor designs including linear force sensors,
fibre-interfaced nonlinear emitters, and driven-dissipative many-body sensors,
and demonstrate that it can be robustly implemented under realistic
experimental imperfections.
