Introduction to repeated quantum measurements

In these 4 hours, I will introduce the main results in the theory of quantum repeated measurements.

Given the background and allowed time, I discuss the following topics.
1- Quantum Instruments and repeated quantum measurements dynamical system definitions
2- Quantum channel Perron-Frobenius theorem, ergodicity and mixing of the dynamical system
3- Limit theorems through the spectral and martingale approximation methods
4- Large deviation principle and hypothesis testing
5- Quantum trajectories, purification and limit theorems

This initiative is part of the "PhD Lectures" activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.