#### The PhD lectures take place on Wednesday morning, usually at 11:30 Italian time

*December 13th, 2023*

#### Stefano Marcantoni (Université Côte d'Azur, LJAD)

#### Introduction to the theory of open quantum systems

In this lecture, I will introduce the framework commonly used to describe the dynamics of open quantum systems. This is based on completely positive dynamical maps and markovian master equations in GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) form. I will discuss the general structure of the latter for an N-level system and present some simple examples. Among them, I will focus on the so-called "Davies generator" induced by the interaction with a thermal Bose field, whose rigorous derivation was originally given by Davies in the van Hove scaling limit and has been recently improved by Merkli uniformly in time. Finally, I will also mention a few directions of current research and point to some relevant literature.

*November 8th, 2023*

#### Ángela Capel Cuevas (Universität Tübingen)

#### Quantum entropy and trace inequalities

In this talk, I will give an elementary introduction to the subject of quantum entropies and trace inequalities, with a special focus on results that are relevant to quantum information theory. First, we will discuss various different notions of quantum entropies that extend those of classical entropies, and we will show several of their fundamental properties, in particular under the application of quantum channels. We will put a special focus on those properties that differ from their classical counterparts. Next, we will describe some contexts within quantum Shannon theory in which the use of quantum entropies is fundamental, such as for quantum hypothesis testing or to estimate quantum channel capacities.

Lecture Notes - Lecture Notes (highlighted)