Alice and Bob meet Banach : the interface of asymptotic geometric analysis and quantum information theory
 Responsibility
 Guillaume Aubrun, Stanisław J. Szarek.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Copyright notice
 ©2017
 Physical description
 xxi, 414 pages : illustrations ; 26 cm.
 Series
 Mathematical surveys and monographs ; no. 223.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA3 .A4 V.223  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Aubrun, Guillaume, 1981 author.
 Contributor
 Szarek, Stanisław J., author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 381408) and index.
 Contents

 Alice and Bob: Mathematical Aspects of Quantum Information: Notation and basic conceptsElementary convex analysisThe mathematics of quantum information theoryQuantum mechanics for mathematiciansBanach and His spaces: Asymptotic Geometric Analysis Miscellany: More convexityMetric entropy and concentration of measure in classical spacesGaussian processes and random matricesSome tools from asymptotic geometric analysisThe Meeting: AGA and QIT: Entanglement of pure states in high dimensionsGeometry of the set of mixed statesRandom quantum statesBell inequalities and the GrothendieckTsirelson inequalityPOVMs and the distillability problemGaussian measures and Gaussian variablesClassical groups and manifoldsExtreme maps between Lorentz cones and the $S$lemmaPolarity and the Santalo point via duality of conesHints to exercisesBibliographyNotationIndex.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twentyfirst century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, highdimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, especially the part that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this userfriendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.", {"source"=>"(source: Nielsen Book Data)"}, "9781470434687", "20171009"]
Subjects
 Subject
 Geometric analysis.
 Quantum theory.
 Functional analysis > Normed linear spaces and Banach spaces; Banach lattices > Normed linear spaces and Banach spaces; Banach lattices.
 Convex and discrete geometry > General convexity > General convexity.
 Quantum theory > Axiomatics, foundations, philosophy > Axiomatics, foundations, philosophy.
 Functional analysis > Normed linear spaces and Banach spaces; Banach lattices > Local theory of Banach spaces.
 Functional analysis > Normed linear spaces and Banach spaces; Banach lattices > Probabilistic methods in Banach space theory.
 Convex and discrete geometry > Discrete geometry > Packing and covering in $n$ dimensions.
 Probability theory and stochastic processes > Probability theory on algebraic and topological structures > Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
 Quantum theory > Axiomatics, foundations, philosophy > Quantum coherence, entanglement, quantum correlations.
 Geometric analysis.
 Quantum theory.
 Functional analysis > Normed linear spaces and Banach spaces; Banach lattices > Normed linear spaces and Banach spaces; Banach lattices.
 Convex and discrete geometry > General convexity > General convexity.
 Quantum theory > Axiomatics, foundations, philosophy > Axiomatics, foundations, philosophy.
 Convex and discrete geometry > Discrete geometry > Packing and covering in $n$ dimensions.
 Probability theory and stochastic processes > Probability theory on algebraic and topological structures > Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
 Geometric analysis.
 Quantum theory.
Bibliographic information
 Publication date
 2017
 Copyright date
 2017
 Title Variation
 Interface of asymptotic geometric analysis and quantum information theory
 Series
 Mathematical surveys and monographs ; volume 223
 ISBN
 9781470434687 (alk. paper)
 1470434687 (alk. paper)