Categories and quantum informatics
Monoidal categories form compositional denotational semantics for information processing protocols. We introduce the idea behind category theory, the breadth of its scope, and explain why it is a good idea to abstract away from specific hard-coded set-theoretic structures. Specific attention is paid to the graphical calculus, which makes the topic visually apparent, and lets us 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.
This 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.
- C. Heunen. Categories and quantum informatics. Slides from the EWSCS 2018 course.
- Lecture 1: Monoidal categories and graphical calculus [pdf]
- Lecture 2: Scalars, daggers, duals, teleportation [pdf]
- Lecture 3: Monoids and Frobenius structures [pdf]
- Lecture 4: Complementarity and ZX-calculus [pdf]
- Videos from the lectures (large, unedited files) [mp4, password-protected]
April 10, 2020 22:35 Europe/Helsinki (GMT +03:00)
local organizers, ewscs18(at)cs.ioc.ee
EWSCS'18 page: http://cs.ioc.ee/ewscs/2018/