Matteo Paris is a full professor at the Department of Physics, University of Milano, where he founded and lead the Applied Quantum Mechanics research group (http://users.unimi.it/aqm), currently composed of twenty people, carrying on theoretical and experimental research on quantum technology, quantum optics and foundations of quantum mechanics.
He is a theoretician working in close collaborations with experimentalists on quantum information, quantum optics and foundations of quantum mechanics. In these fields he is author of about 300 publications on international journals, which received more than 8500 citations, with about 60 invited talks and seminars; his
h-index is currently 47 (Google scholar). His main contributions are in the fields of quantum estimation of states and operations, generation and application of
entanglement and more general quantum correlations, quantum information processing, open quantum systems, interferometry and high-precision measurements.
Quantum estimation theory (QET) is a powerful tool for quantum sensing metrology and the search of new physics. This tutorial is devoted to QET and it is divided in two parts.
In the first part, I provide an invitation to QET, introducing ideas and methods from scratch, and providing examples of application.
In the second part, I go back to foundation of QET and emphasize that a crucial assumption to prove the quantum Cramer-Rao theorem is that the unknown parameters label the possible states of the system, while they influence neither the sample space of outcomes, nor the measurement aimed at extracting information on the parameters itself. However, there are relevant estimation problems where this assumption does not hold and an alternative approach should be developed to find the genuine ultimate bound to precision of quantum measurements. We investigate physical situations where there is an intrinsic dependence of the measurement strategy on the parameter, and find that quantum-enhanced measurements may be more precise than previously thought.