"Categories for Quantum Theory" book

"Categories for Quantum Theory" book

[Chris Heunen]

Dear colleagues,

We're delighted to announce that our book "Categories for Quantum
Theory" has finally been published with Oxford University Press, in
the series Oxford Graduate Texts in Mathematics. We hope you may be
interested in it, and would love your feedback!

https://global.oup.com/academic/product/categories-for-quantum-theory-9780198739616

PR summary: 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. This text lays the
foundation for this categorical quantum mechanics, with an emphasis on
the graphical calculus which makes computation intuitive. Biproducts
and dual objects are introduced and used to model superposition and
entanglement, with quantum teleportation studied abstractly using
these structures. Monoids, Frobenius structures and Hopf algebras are
described, and it is shown how they can be used to model classical
information and complementary observables. The CP construction, a
categorical tool to describe probabilistic quantum systems, is also
investigated. The last chapter introduces higher categories, surface
diagrams and 2-Hilbert spaces, and shows how the language of duality
in monoidal 2-categories can be used to reason about quantum
protocols, including quantum teleportation and dense coding.

Prior knowledge of linear algebra, quantum information or category
theory would give an ideal background for studying this text, but it
is not assumed, with essential background material given in a
self-contained introductory chapter. Throughout the text links with
many other areas are highlighted, such as representation theory,
topology, quantum algebra, knot theory, and probability theory, and
nonstandard models are presented, such as sets and relations. All
results are stated rigorously, and full proofs are given as far as
possible, making this book an invaluable reference for modern
techniques in quantum logic, with much of the material not available
in any other textbook.

Kind regards,
Chris Heunen and Jamie Vicary

-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.



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