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Quantum Symmetries : Metabief, France 2014 /

Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantu...

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Bibliographic Details
Main Authors: Aubrun, Guillaume (Author)
Corporate Authors: SpringerLink (Online service)
Group Author: Skalski, Adam (Editor); Speicher, Roland; Franz, Uwe
Published: Springer International Publishing : Imprint: Springer,
Publisher Address: Cham :
Publication Dates: 2017.
Literature type: eBook
Language: English
Series: Lecture Notes in Mathematics, 2189
Subjects:
Mathematics.
Functional analysis.
Convex geometry.
Discrete geometry.
Probabilities.
Quantum Physics.
Probability Theory and Stochastic Processes.
Convex and Discrete Geometry.
Online Access: http://dx.doi.org/10.1007/978-3-319-63206-3
Summary: Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.
Carrier Form: 1 online resource (IX, 119 pages): illustrations.
ISBN: 9783319632063
Index Number: QA319
CLC: O177
Contents: 1 Introduction -- 2 Free Probability and Non-Commutative Symmetries -- 3 Quantum Symmetry Groups and Related Topics -- 4 Quantum Entanglement in High Dimensions -- References -- Index.

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