'Pre-quantum information and communication' and 'Quantum information and communication'

Information Theory, established in Claude Shannon's 1948 landmark paper, provides a theoretical view on classical and quantum communication systems. While Shannon's original work considered an asymptotic setting where unbounded transmission delays are acceptable, Finite-Length Information Theory offers a more refined view that takes transmission delays into account. This is specially relevant in quantum systems, where existing technology does not allow to perform optimal measurements over a large set of quantum states. This course introduces students to Finite-Length Information Theory and equips them with the main mathematical tools required to analyze performance bounds both in classical and quantum systems. In particular, students will learn about: - Peformance bounds for classical and quantum communication systems based on random coding and/or optimal decision theory. - Asymptotic and numerical methods to analyze these bounds. - Their applications in practical communication systems.

1. Performance bounds in Finite-Length Information Theory 1.1 Random coding bounds 1.2 Quantum hypothesis testing and optimal decision theory 2. Asymptotic analysis 2.1 The channel coding problem: Capacity and strong converses 2.2 Large deviations and error exponents 2.3 The central limit theory and second-order coding rates 3. Evaluation of performance bounds 3.1 Semidefinite and linear programming 3.2 Saddlepoint approximations 4. Applications to practical communication systems 4.1 Additive Gaussian noise channels 4.2 Bosonic channels

LECTURES Lectures provide an overview of the main concepts and analytical tools in Finite-Length Information Theory. The classes are mainly taught at the board, aided by slides or and audiovisual media for the illustration of certain topics. EXERCISES To deepen the understanding of the taught material, students are provided with problem sets which need to be solved at home and handed in once a month. These solutions will be graded from 1 to 10, and the average grade over the whole semester will constitute part the grade of the continuous assessment.