LEADER 04041nam 22007095 450 001 996466521003316 005 20200705130201.0 010 $a3-319-63206-X 024 7 $a10.1007/978-3-319-63206-3 035 $a(CKB)4100000000882280 035 $a(DE-He213)978-3-319-63206-3 035 $a(MiAaPQ)EBC6300816 035 $a(MiAaPQ)EBC5610748 035 $a(Au-PeEL)EBL5610748 035 $a(OCoLC)1007130065 035 $a(PPN)220120978 035 $a(EXLCZ)994100000000882280 100 $a20171013d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum Symmetries$b[electronic resource] $eMetabief, France 2014 /$fby Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (IX, 119 p. 18 illus., 3 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2189 311 $a3-319-63205-1 327 $a1 Introduction -- 2 Free Probability and Non-Commutative Symmetries -- 3 Quantum Symmetry Groups and Related Topics -- 4 Quantum Entanglement in High Dimensions -- References -- Index. 330 $aProviding an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2189 606 $aFunctional analysis 606 $aQuantum physics 606 $aProbabilities 606 $aConvex geometry  606 $aDiscrete geometry 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 615 0$aFunctional analysis. 615 0$aQuantum physics. 615 0$aProbabilities. 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 14$aFunctional Analysis. 615 24$aQuantum Physics. 615 24$aProbability Theory and Stochastic Processes. 615 24$aConvex and Discrete Geometry. 676 $a515.7 700 $aAubrun$b Guillaume$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755750 702 $aSkalski$b Adam$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSpeicher$b Roland$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aFranz$b Uwe$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466521003316 996 $aQuantum Symmetries$91984167 997 $aUNISA