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171103 ||| eng |
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|a 9783319632063
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| 100 |
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|a Aubrun, Guillaume
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| 245 |
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|a Quantum Symmetries
|h Elektronische Ressource
|b Metabief, France 2014
|c by Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz
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| 250 |
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|a 1st ed. 2017
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| 260 |
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|a Cham
|b Springer International Publishing
|c 2017, 2017
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| 300 |
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|a IX, 119 p. 18 illus., 3 illus. in color
|b online resource
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| 505 |
0 |
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|a 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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| 653 |
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|a Functional analysis
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| 653 |
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|a Convex and Discrete Geometry
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Convex geometry
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| 653 |
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|a Quantum Physics
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| 653 |
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|a Quantum physics
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| 653 |
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|a Discrete geometry
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| 653 |
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|a Probability Theory and Stochastic Processes
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| 653 |
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|a Probabilities
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| 700 |
1 |
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|a Skalski, Adam
|e [author]
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| 700 |
1 |
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|a Speicher, Roland
|e [author]
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| 700 |
1 |
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|a Franz, Uwe
|e [editor]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Lecture Notes in Mathematics
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-319-63206-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515.7
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| 520 |
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|a 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
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