23rd Estonian Winter School in Computer Science (EWSCS)
XXIII Eesti Arvutiteaduse Talvekool

Palmse, Estonia, March 4 - 9, 2018

Chris Heunen

School of Informatics
University of Edinburgh
UK

Categories and quantum informatics

Abstract

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.

Course materials

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EWSCS'18 page: http://cs.ioc.ee/ewscs/2018/