Adaptive Quantum Metrology under General Markovian Noise

We consider a general model of unitary parameter estimation in the presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In the absence of noise, the unitary parameter can be estimated with precision scaling as 1/T, where T is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum master equation, implying, at most, 1/√T scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction-like protocol must satisfy in order to regain the 1/T precision scaling in case the above-mentioned algebraic condition is not satisfied. Furthermore, we apply the methods developed to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of nonlinear metrological models.