Alice and Bob Meet Banach

The Interface of Asymptotic Geometric Analysis and Quantum Information Theory

AvGuillaume Aubrun,Stanislaw J. Szarek

Häftad, Engelska, 2017

Del i serien Mathematical Surveys and Monographs

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Beskrivning

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first 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, high-dimensional 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, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly 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.

Produktinformation

Utgivningsdatum:2017-10-31
Format:Häftad
Språk:Engelska
Serie:Mathematical Surveys and Monographs
Antal sidor:414
Förlag:American Mathematical Society
ISBN:9781470477967

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Guillaume Aubrun, Universite Claude Bernard Lyon 1, Villeurbanne, France.Stanislaw J. Szarek, Case Western Reserve University, Cleveland, OH, and Sorbonne Universite, Paris, France.

Recensioner i media

“[This book] will be an invaluable reference to scientists working on the more mathematical aspects of quantum information theory.” - Mary Beth Ruskai, Zentralblatt MATH“A wide variety of audiences would be interested in this book: Parts II or III would be suitable for a graduate course on QIT from the perspective of functional analysis, convex geometry, or random matrix theory, or on the applications of AGA. With a mix of classical and recent results, as well as the concise treatment of the subject areas, the book could be used as a reference book for researchers working in this area. Furthermore, the large number of exercises, with an appendix of hints, would make it suitable for an independent study.” - Sarah Plosker, Mathematical Reviews

Innehållsförteckning

Alice and Bob: Mathematical Aspects of Quantum InformationNotation and basic conceptsElementary convex analysisThe mathematics of quantum information theoryQuantum mechanics for mathematiciansBanach and His spaces: Asymptotic Geometric Analysis MiscellanyMore convexityMetric entropy and concentration of measure in classical spacesGaussian processes and random matricesSome tools from asymptotic geometric analysisThe Meeting: AGA and QITEntanglement of pure states in high dimensionsGeometry of the set of mixed statesRandom quantum statesBell inequalities and the Grothendieck-Tsirelson 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 exercisesNotation