Revisiting continuous measurement metrology

The continuous monitoring of driven-dissipative systems offers new avenues where one might find a quantum advantage in metrology. To study the sensitivity of continuous quantum sensors, we map the problem of calculating the QFI of continuously-monitored systems to a qubit dephasing problem. This allows us to identify characteristic timescales associated with the integration time of the sensor, and a timescale-independent contribution deriving from the properties of the sensor’s steady state. Focusing on collective spins, we then proceed to identify a hierarchy of systems displaying Heisenberg scalings, distinguished by the type of entanglement required and the difficulty of engineering the optimal measurement.