Designing open quantum systems for enabling quantum-enhanced sensing through classical measurements

Quantum systems in nonequilibrium conditions, where coherent many-body interactions compete with dissipative effects, can feature rich phase diagrams and emergent critical behavior. Associated collective effects, together with the continuous observation of quanta dissipated into the environment - typically photons - allow one to achieve quantum-enhanced parameter estimation. However, protocols for tapping this enhancement typically involve intricate measurements on the combined system-environment state. Here, we show that many-body quantum enhancement can in fact be obtained through classical measurements such as photon counting and homodyne detection. We illustrate this in detail for a class of open spin-boson models, which can be realized in trapped-ion or cavity QED setups. Our findings highlight a route toward the design of systems that enable a practical implementation of quantum-enhanced metrology through continuous classical measurements.