https://perso.telecom-paristech.fr/rioul/cours/quantum-athens.html

https://perso.telecom-paristech.fr/rioul/cours/quantum/flyer-athens.pdf

This course offers a step-by-step introduction to the mathematical foundations of quantum information, starting from simple postulates within finite-dimensional systems. A central emphasis is placed on quantum measurement and its inherently probabilistic nature, from which the linear evolution of quantum states and the derivation of the Schrödinger differential equation for isolated systems can be mathematically derived.

The course then addresses more realistic scenarios involving noise or interactions with an external environment. In such settings, quantum states are described by density matrices, while their transformations are modeled by quantum channels, together with a general framework for quantum measurements.

If time permits, the course will also explore mathematical tools used to define and compare distances, divergences or similarities between quantum states, highlighting their connections with quantum channels and measurement processes.

As a prerequisite, participants are recommended to be familiar with linear algebra, complex numbers, and elementary probability theory and information theory. It should be noted that, although the course does not presuppose knowledge of Hilbert spaces, it does presuppose a fairly comprehensive knowledge of finite-dimensional complex scalar product spaces (also known as Hermitian spaces, the natural generalization of Euclidean spaces over the complex numbers). This course does not presuppose any knowledge on quantum physics but focuses on the mathematics of quantum information.

The course is intended for a broad audience of enthusiast students from all fields who wish to develop a solid theoretical understanding of the principles underlying quantum computing and quantum information.