12 Settembre, 2017 15:00

Sezione di Probabilità Quantistica

The theory of quantum statistical comparison with some applications to quantum information science

Francesco Buscemi, Nagoya University

Aula Seminari III piano

In mathematical statistics a central role is played by the notion of statistical models (or, equivalently, statistical experiments). These objects, which can be imagined as families of probability distributions, are often used to describe the statistician's state of knowledge about an unknown parameter. It is then natural to compare statistical models on the basis of their "information content." This kind of problems led in the 1950s to the formulation of a whole new theory, sometimes named "statistical comparison theory," which soon developed into a very deep field with many applications, ranging from mathematical statistics, to physics and economics. In this lecture I will present an overview of the basic ideas of statistical comparison, some possible generalizations to the quantum setting, and a few applications in quantum thermodynamics, entanglement theory, quantum measurement theory, and the theory of open quantum systems.