Mathematical Aspects of Quantum Information Theory (PhD course)
Description
The course took place in winter 2023, in the PhD program in mathematics at Sapienza University, Rome. The goal is to provide an introduction to mathematical methods and concepts in quantum information theory (in finite dimension). The program is divided into the following points:
- Postulates of Quantum Mechanics: pure and mixed states, observables, tensor products and entanglement (slides)
- Open quantum systems: CPTP maps, quantum Markov semigroup and generators (slides)
- Inequalities: uncertainty, monotonicity, convexity (slides)
- Distances between quantum states: trace distance, fidelity, quantum optimal transport (slides)
- Quantum entropy and its properties (slides)
- THe Schumacher-Westmoreland and Holevo coding theorem (slides).
Main bibliographical references are: - Nielsen, Michael A., and Isaac L. Chuang. Quantum computation and quantum information. Cambridge university press, 2010. - Holevo, Alexander S. Quantum systems, channels, information: a mathematical introduction. Walter de Gruyter GmbH & Co KG, 2019.
Teaching material
Lecture notes: please notify me about possible typos and inaccuracies.
Slides: 1, 2, 3, 4, 5, 6. Beware: there are typos and inaccuracies, please refer to the lecture notes.
