03094nam a2200457 i 4500991003560719707536m o d cr cnu|||unuuu181019s2017 sz a o 101 0 eng d9783319632063331963206X10.1007/978-3-319-63206-3b14351900-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng539.72523AMS 81-02LC QC174.17.S9Aubrun, Guillaume755750Quantum symmetries[e-book] :Metabief, France 2014 /Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe FranzCham, Switzerland :Springer,20171 online resource (ix, 119 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2189Includes index1 Introduction ; 2 Free Probability and Non-Commutative Symmetries ; 3 Quantum Symmetry Groups and Related Topics ; 4 Quantum Entanglement in High Dimensions ; References ; IndexProviding 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 theorySymmetry (Physics)CongressesMathematical physicsCongressesSkalski, Adamauthorhttp://id.loc.gov/vocabulary/relators/aut755751Speicher, Rolandauthorhttp://id.loc.gov/vocabulary/relators/aut303453Franz, UweSpringerLink (Online service)Printed edition:9783319632056https://link.springer.com/book/10.1007/978-3-319-63206-3An electronic book accessible through the World Wide Web.b1435190003-03-2219-10-18991003560719707536Quantum symmetries1522938UNISALENTOle01319-10-18m@ -engsz 00