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000727487 020__ $$a9783319167183$$qelectronic book
000727487 020__ $$a3319167189$$qelectronic book
000727487 020__ $$z9783319167176
000727487 0247_ $$a10.1007/978-3-319-16718-3$$2doi
000727487 035__ $$aSP(OCoLC)ocn910663209
000727487 035__ $$aSP(OCoLC)910663209
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000727487 050_4 $$aQC174.17.M35
000727487 08204 $$a530.1201/51$$223
000727487 1001_ $$aGupta, Ved Prakash,$$eauthor.
000727487 24514 $$aThe functional analysis of quantum information theory$$h[electronic resource] :$$ba collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter /$$cVed Prakash Gupta, Prabha Mandayam, V.S. Sunder.
000727487 264_1 $$aCham :$$bSpringer,$$c2015.
000727487 300__ $$a1 online resource (xi, 139 pages).
000727487 336__ $$atext$$btxt$$2rdacontent
000727487 337__ $$acomputer$$bc$$2rdamedia
000727487 338__ $$aonline resource$$bcr$$2rdacarrier
000727487 4901_ $$aLecture notes in physics,$$x0075-8450 ;$$vvolume 902
000727487 504__ $$aIncludes bibliographical references and index.
000727487 5050_ $$aPreface -- Operator Spaces -- Entanglement in Bipartite Quantum States -- Operator Systems -- Quantum Information Theory -- Index -- Bibliography.
000727487 506__ $$aAccess limited to authorized users.
000727487 520__ $$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.
000727487 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 4, 2015).
000727487 650_0 $$aQuantum theory$$xMathematics.
000727487 650_0 $$aQuantum computing.
000727487 7001_ $$aMandayam, Prabha,$$eauthor.
000727487 7001_ $$aSunder, V. S.,$$eauthor.
000727487 830_0 $$aLecture notes in physics ;$$vvolume 902.
000727487 852__ $$bebk
000727487 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-16718-3$$zOnline Access$$91397441.1
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