Lectures and Exercises: H. Chau Nguyen (email)

Time and place: 14:00-16:00 Wednesday, Room D115-ENC.

### Prerequisites

- Basic intuitive knowledge of quantum mechanics
- Basic concepts of general algebra and linear algebra

### Contents

- Classical and quantum systems: observables and states
- Definition of entropy
- The statistical interpretation of entropy
- Quantum processes
- Monotonicity of the relative entropy: the statement and the consequences
- Monotonicity of the relative entropy: lessons from the proof
- Bipartite system: subadditivity, mutual information, conditional entropy
- Application: the classical capacity of communication channels
- Application: thermodynamics entropy and the Landauer’s principle
- Multipartite system: strong subadditivity

### Scripts (password required):

- First part (ocassionally updated): quantum-entropy-light.pdf

### Exercises: integrated in the classes

### References

- Petz, D.,
*“Quantum information theory and quantum statistics”*, Springer 2008.

The content is generally good, but one has to be careful with some technical definitions and typos. - Ohya, M. and Petz, D.,
*“Quantum entropy and its use”*, Springer 1993.

This is a somewhat advanced version of the above one. The contents are much richer, but also a lot denser. - Nilsen, M. A. and Chuang, I. L.
*“Quantum computation and quantum information”.*Cambridge 2010.

This book is kind of classic. The contents are rich, but the structure is perhaps not optimal. - Cover, T. and Thomas, J. A.,
*“Elements of information theory”*, John Wiley & Son 2006.

Classics for information theory: rich, clean, clear.