Quantum Estimation and Control for Advanced Noisy Metrology

In recent years, the idea of building quantum technologies has quickly moved from being an intellectual curiosity to a practical reality and quantum metrology and quantum sensors are prominent ones, already in use in scientific and commercial applications. The underlying idea is to exploit genuinely quantum effects to perform extremely accurate measurements, with a precision not achievable by classical means.While many important theoretical and experimental milestones have already been reached, there are still many open theoretical questions left on the path to understanding the ultimate capabilities of quantum metrology, especially in realistic operating conditions.We have identified three main pillars that are currently subject to very active research: i) understanding the ultimate limits of the quantum estimation of multiple parameters simultaneously, either because all of them are of practical interest, or because a full prior characterization of additional system's parameters is not possible; ii) assessing the impact of environmental noise on the quantum probe, in particular beyond the standard assumption of uncorrelated noise; iii) understanding the limits of metrological schemes based on time-continuous measurements, nowadays feasible in many physical systems (e.g. superconducting qubits, optomechanics), which open the possibility to perform measurement-based feedback control on the system.The overarching goal of this action is to advance the state of the art in these three areas and to connect these three pillars, by devising new theoretical tools to assess the ultimate precision limits in novel and physically relevant scenarios. These tools will be rooted in quantum estimation theory and quantum control theory and they will provide fundamental benchmarks for the next generation of quantum sensors.