This short course provides an introduction to both classical and quantum information theory, beginning with the fundamental notion of information and its role in the description of physical systems. We first introduce the basic concepts of information theory and then illustrate their relevance through an application to deterministic dynamical systems, where information-theoretic ideas naturally lead to the definition of the Kolmogorov-Sinai entropy as a measure of dynamical complexity. Having established this motivation, we develop the foundations of classical information theory following the framework introduced by Claude Shannon in his seminal 1948 work. We define Shannon entropy and discuss its operational significance, introducing the concept of classical typicality and proving Shannon's first coding theorem (the noiseless coding theorem). We then extend the discussion to communication over noisy channels by introducing joint entropy, conditional entropy, and mutual information, culminating in Shannon's second coding theorem. The second part of the course provides an introduction to quantum information theory. We define the fundamental quantum information measures, with particular emphasis on the von Neumann entropy and related quantities, and discuss the concept of quantum typicality as the cornerstone of quantum data compression. Finally, we conclude with an introduction to quantum quantum key distribution as an example of how quantum mechanics enables information-processing tasks with no classical counterpart.
First Class - Introduction
Second Class - Informational description of deterministic dynamical systems
Third Class - First Shannon coding theorem
Fourth Class - Classical typicality
Fifth Class - Second Shannon coding theorem
Sixth Class - Elements of quantum information
Seventh Class - Quantum typicality
Eighth Class - Quantum key distribution