LEADER 03094nam a2200457 i 4500 001 991003560719707536 006 m o d 007 cr cnu|||unuuu 008 181019s2017 sz a o 101 0 eng d 020 $a9783319632063 020 $a331963206X 024 7 $a10.1007/978-3-319-63206-3 035 $ab14351900-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a539.725$223 084 $aAMS 81-02 084 $aLC QC174.17.S9 100 1 $aAubrun, Guillaume$0755750 245 10$aQuantum symmetries$h[e-book] :$bMetabief, France 2014 /$cGuillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz 264 1$aCham, Switzerland :$bSpringer,$c2017 300 $a1 online resource (ix, 119 pages) :$billustrations (some color) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2189 500 $aIncludes index 505 0 $a1 Introduction ; 2 Free Probability and Non-Commutative Symmetries ; 3 Quantum Symmetry Groups and Related Topics ; 4 Quantum Entanglement in High Dimensions ; References ; Index 520 $aProviding an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory 650 0$aSymmetry (Physics)$vCongresses 650 0$aMathematical physics$vCongresses 700 1 $aSkalski, Adam$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0755751 700 1 $aSpeicher, Roland$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0303453 700 1 $aFranz, Uwe 710 2 $aSpringerLink (Online service) 776 08$iPrinted edition:$z9783319632056 856 41$uhttps://link.springer.com/book/10.1007/978-3-319-63206-3$zAn electronic book accessible through the World Wide Web 907 $a.b14351900$b03-03-22$c19-10-18 912 $a991003560719707536 996 $aQuantum symmetries$91522938 997 $aUNISALENTO 998 $ale013$b19-10-18$cm$d@ $e-$feng$gsz $h0$i0