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OverviewMonoidal 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. Full Product DetailsAuthor: Chris Heunen (Reader, Reader, University of Edinburgh) , Jamie Vicary (Royal Society University Research Fellow, Royal Society University Research Fellow, University of Birmingham)Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 16.20cm , Height: 2.40cm , Length: 23.60cm Weight: 0.682kg ISBN: 9780198739623ISBN 10: 0198739621 Pages: 338 Publication Date: 19 November 2019 Audience: College/higher education , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsAuthor InformationChris Heunen started his undergraduate studies at the University of Nijmegen, where he received MSc degrees in both Computer Science and Mathematics, and in 2009 a PhD degree. He then did postdoctoral research at the University of Oxford and the California Institute of Technology. His work was awarded the 2012 Birkhoff-von Neumann prize for research on quantum structures. In 2015 he joined the University of Edinburgh. Jamie Vicary did an undergraduate degree in Physics in Oxford, followed by the Part III Mathematics course in Cambridge. He did a PhD in category theory and quantum information with Christopher Isham at Imperial College London, which was awarded in 2009. Since that time he has done research into the mathematical foundations of quantum computation, with positions in Oxford, Singapore and Birmingham. Tab Content 6Author Website:Countries AvailableAll regions |