Luogo: Aula Maxwell Relatore: Matteo Paris E-Mail: raffaella.burioni@fis.unipr.it Abstract: Several quantities of interest in physics are non-linear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. In this lecture I review local quantum estimation theory, which allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices, e.g. in quantum technology. We introduce the concepts of symmetric logarithmic derivative and quantum Fisher information, and provide explicit formulas for relevant families of quantum states. We also illustrate the connection between the optmization procedure and the geometry of quantum statistical models. Finally, few applications, ranging from quantum optics to critical systems are presented.
