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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Categories for Quantum Theory - An Introduction (Paperback)
Loot Price: R1,481
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Categories for Quantum Theory - An Introduction (Paperback)
Series: Oxford Graduate Texts in Mathematics
Expected to ship within 9 - 15 working days
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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.
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