Categories for Quantum Theory: An Introduction Chris Heunen

Categories for Quantum Theory: An Introduction – Ebook Instant Download/Delivery ISBN(s): 9780198739616,9780198739623,0198739613,0198739621

Product details:

• ISBN-10 ‏ : ‎ 0198739613
• ISBN-13 ‏ : ‎ 978-0198739616
• Author(s): Chris Heunen, Jamie Vicary

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.

Table contents:

1 Monoidal Categories

2 Linear Structure

3 Dual Objects

4 Monoids and Comonoids

5 Frobenius Structures

6 Complementarity

7 Complete Positivity

8 Monoidal 2-Categories

Notes and Further Reading

References

Index

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