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Categories for Quantum Theory: An Introduction

Chris Heunen and Jamie Vicary

Abstract

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures an ... More

Keywords: Category, Quantum theory, Graphical calculus, Quantum teleportation, Compositionality, Higher categories, Tensor product, Hopf algebras, Frobenius algebras

Bibliographic Information

Print publication date: 2019 Print ISBN-13: 9780198739623
Published to Oxford Scholarship Online: January 2020 DOI:10.1093/oso/9780198739623.001.0001

Authors

Affiliations are at time of print publication.

Chris Heunen, author
Reader, University of Edinburgh

Jamie Vicary, author
Royal Society University Research Fellow, University of Birmingham