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The Functional Analysis of Quantum Information Theory

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 (Autoren)

Buch | Softcover

XI, 139 Seiten

2015 | 2015
Springer International Publishing (Verlag)
978-3-319-16717-6 (ISBN)

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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.

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

"This volume is a collection of notes from a two-week workshop ... . the contributions from the four workshop speakers are quite well written and the editors have achieved a high level of consistency in style and terminology. ... This collection will be of interest to researchers in physics, mathematics, and theoretical computer science." (Kevin J. Compton, Mathematical Reviews, January, 2016)

Erscheint lt. Verlag	10.6.2015
Reihe/Serie	Lecture Notes in Physics
Zusatzinfo	XI, 139 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	254 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Bipartite quantum states • Hilbert space operators • Operator spaces and systems • quantum entropy • Quantum functional analysis • Quantum Information Theory • Tensor products of C -algebras • Tensor products of C*-algebras
ISBN-10	3-319-16717-0 / 3319167170
ISBN-13	978-3-319-16717-6 / 9783319167176
Zustand	Neuware