04041nam 22007095 450 99646652100331620200705130201.03-319-63206-X10.1007/978-3-319-63206-3(CKB)4100000000882280(DE-He213)978-3-319-63206-3(MiAaPQ)EBC6300816(MiAaPQ)EBC5610748(Au-PeEL)EBL5610748(OCoLC)1007130065(PPN)220120978(EXLCZ)99410000000088228020171013d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierQuantum Symmetries[electronic resource] Metabief, France 2014 /by Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (IX, 119 p. 18 illus., 3 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;21893-319-63205-1 1 Introduction -- 2 Free Probability and Non-Commutative Symmetries -- 3 Quantum Symmetry Groups and Related Topics -- 4 Quantum Entanglement in High Dimensions -- References -- Index.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.Lecture Notes in Mathematics,0075-8434 ;2189Functional analysisQuantum physicsProbabilitiesConvex geometry Discrete geometryFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Quantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Convex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014Functional analysis.Quantum physics.Probabilities.Convex geometry .Discrete geometry.Functional Analysis.Quantum Physics.Probability Theory and Stochastic Processes.Convex and Discrete Geometry.515.7Aubrun Guillaumeauthttp://id.loc.gov/vocabulary/relators/aut755750Skalski Adamauthttp://id.loc.gov/vocabulary/relators/autSpeicher Rolandauthttp://id.loc.gov/vocabulary/relators/autFranz Uweedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK996466521003316Quantum Symmetries1984167UNISA