The functional analysis of quantum information theory [electronic resource] : a collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter / Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder.
Gupta, Ved Prakash, author.; Mandayam, Prabha, author.; Sunder, V. S., author.
2015
QC174.17.M35
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Title The functional analysis of quantum information theory [electronic resource] : a collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter / Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder.
Author Gupta, Ved Prakash, author.
ISBN 9783319167183 electronic book
3319167189 electronic book
9783319167176
DOI https://doi.org/10.1007/978-3-319-16718-3
Published Cham : Springer, 2015.
Language English
Description 1 online resource (xi, 139 pages).
Item Number 10.1007/978-3-319-16718-3 doi
Call Number QC174.17.M35
Dewey Decimal Classification 530.1201/51
Summary This 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 4, 2015).
Added Author Mandayam, Prabha, author.
Sunder, V. S., author.
Series Lecture notes in physics ; volume 902.
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Preface
Operator Spaces
Entanglement in Bipartite Quantum States
Operator Systems
Quantum Information Theory
Index
Bibliography.

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