國立高雄大學圖資館 |

Language: English

Back

The functional analysis of quantum i...

Gupta, Ved Prakash.

The functional analysis of quantum information theorya collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The functional analysis of quantum information theoryby Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder.
Reminder of title:	a collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter /
Author:	Gupta, Ved Prakash.
other author:	Mandayam, Prabha.
Published:	Cham :Springer International Publishing :2015.
Description:	xi, 139 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Quantum theoryMathematics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-16718-3
ISBN:	9783319167183 (electronic bk.)

The functional analysis of quantum information theorya collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter /
Gupta, Ved Prakash.

The functional analysis of quantum information theorya collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter /[electronic resource] :by Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder. - Cham :Springer International Publishing :2015. - xi, 139 p. :ill., digital ;24 cm. - Lecture notes in physics,v.9020075-8450 ;. - Lecture notes in physics ;650..

Preface -- Operator Spaces -- Entanglement in Bipartite Quantum States -- Operator Systems -- Quantum Information Theory -- Index -- Bibliography.

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.

ISBN: 9783319167183 (electronic bk.)

Standard No.: 10.1007/978-3-319-16718-3doiSubjects--Topical Terms:

207816
Quantum theory
--Mathematics.

LC Class. No.: QC174.17.M35

Dewey Class. No.: 530.120151

The functional analysis of quantum information theorya collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter /
LDR:03350nmm a2200325 a 4500 001 469285
003 DE-He213
005 20160105165828.0
006 m d
007 cr nn 008maaau
008 160118s2015 gw s 0 eng d
020 $a 9783319167183 (electronic bk.)
020 $a 9783319167176 (paper)
024 7 $a 10.1007/978-3-319-16718-3 $2 doi
035 $a 978-3-319-16718-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.M35
072 7 $a PHQ $2 bicssc
072 7 $a SCI057000 $2 bisacsh
082 0 4 $a 530.120151 $2 23
090 $a QC174.17.M35 $b G977 2015
100 1 $a Gupta, Ved Prakash. $3 725266
245 1 4 $a The functional analysis of quantum information theory $h [electronic resource] : $b a collection of notes based on lectures by Gilles Pisier, K.R. Parthasarathy, Vern Paulsen and Andreas Winter / $c by Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xi, 139 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in physics, $x 0075-8450 ; $v v.902
505 0 $a Preface -- Operator Spaces -- Entanglement in Bipartite Quantum States -- Operator Systems -- Quantum Information Theory -- Index -- Bibliography.
520 $a 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.
650 0 $a Quantum theory $x Mathematics. $3 207816
650 0 $a Quantum computing. $3 725269
650 1 4 $a Physics. $3 179414
650 2 4 $a Quantum Physics. $3 275010
650 2 4 $a Quantum Computing. $3 573152
650 2 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Mathematical Physics. $3 522725
700 1 $a Mandayam, Prabha. $3 725267
700 1 $a Sunder, V.S. $3 725268
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Lecture notes in physics ; $v 650. $3 451204
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16718-3
950 $a Physics and Astronomy (Springer-11651)