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020 _a9783319167183
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024 7 _a10.1007/978-3-319-16718-3
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072 7 _aSCI057000
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082 0 4 _a530.12
_223
100 1 _aGupta, Ved Prakash.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Functional Analysis of Quantum Information Theory
_h[electronic resource] :
_bA Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter /
_cby Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXI, 139 p.
_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 Physics,
_x0075-8450 ;
_v902
505 0 _aPreface -- Operator Spaces -- Entanglement in Bipartite Quantum States -- Operator Systems -- Quantum Information Theory -- Index -- Bibliography.
520 _aThis book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.
650 0 _aQuantum theory.
650 0 _aMathematical physics.
650 0 _aFunctional analysis.
650 1 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aQuantum Computing.
_0http://scigraph.springernature.com/things/product-market-codes/M14070
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
700 1 _aMandayam, Prabha.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSunder, V.S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319167190
776 0 8 _iPrinted edition:
_z9783319167176
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v902
856 4 0 _uhttps://doi.org/10.1007/978-3-319-16718-3
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c11435
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