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OverviewThis 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. Full Product DetailsAuthor: Ved Prakash Gupta , Prabha Mandayam , V.S. SunderPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 2015 ed. Volume: 902 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 2.409kg ISBN: 9783319167176ISBN 10: 3319167170 Pages: 139 Publication Date: 10 June 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- Operator Spaces.- Entanglement in Bipartite Quantum States.- Operator Systems.- Quantum Information Theory.- Index.- Bibliography.ReviewsThis 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) “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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |