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001 978-3-319-63206-3
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008 171013s2017 gw | s |||| 0|eng d
020 _a9783319632063
_9978-3-319-63206-3
024 7 _a10.1007/978-3-319-63206-3
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
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082 0 4 _a515.7
_223
100 1 _aAubrun, Guillaume.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Symmetries
_h[electronic resource] :
_bMetabief, France 2014 /
_cby Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aIX, 119 p. 18 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2189
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 _aFunctional analysis.
650 0 _aQuantum physics.
650 0 _aProbabilities.
650 0 _aConvex geometry .
650 0 _aDiscrete geometry.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aConvex and Discrete Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21014
700 1 _aSkalski, Adam.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSpeicher, Roland.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aFranz, Uwe.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319632056
776 0 8 _iPrinted edition:
_z9783319632070
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2189
856 4 0 _uhttps://doi.org/10.1007/978-3-319-63206-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c444959
_d444959
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/