Fundamental bounds for the metrology of open quantum systems

Quantum mechanics allows for enhanced measurement precision beyond classical limits by harnessing entanglement and/or long-time coherence. However, these resources are highly sensitive to noise, making their use in open quantum systems particularly challenging. At the same time, optimizing metrological protocols analytically or numerically becomes increasingly difficult as system size and measurement complexity grow. Nonetheless, for quantum systems governed by a master equation, it is possible to derive fundamental, protocol-independent bounds on achievable precision. These bounds provide an objective benchmark to assess existing strategies and identify potential for improvement. In this seminar, I will present these fundamental bounds, first introduced by A. Fujiwara and H. Imai and later extended by R. Demkowicz-Dobrzaski, S. Zhou, L. Jiang, among others. I will illustrate the framework through examples involving interferometry and cavity parameter estimation under photon loss, with particular attention to critical metrology and continuous measurement in the steady-state regime.