Title: Categories and Quantum Informatics

Lecturer: Prof.Chris Heunen (LFCS Univeristy of Edinburgh)

Period: July 10-22

The course begins by introducing the idea behind category theory and the breadth of its scope. Why would it be a good idea to abstract away from specific hard-coded set-theoretic structures, and have compositional denotational semantics, in general? Illustrations from functional programming and categorical methods in logic are given.

We then focus more specifically on monoidal categories. Specific attention is paid to the graphical calculus, which makes the topic visually apparent. The student learns to graphically manipulate algebraic objects such as monoids and Frobenius structures. This allows perfectly rigorous proofs of correctness, and shows the information flow of a protocol that is often hidden behind superfluous details.

Throughout the course, the abstract material is linked to quantum informatics. We will categorically model notions typically thought to belong to quantum theory, such as entanglement, no-cloning, teleportation, and complementarity. But it will turn out some of these notions also make perfect sense in other settings. For example, the very same categorical description of quantum teleportation also describes classical encryption with a one-time pad. We identify characteristics of classical and quantum information, aiming to equip students to choose the right tools and techniques for future problems they may encounter.