Alice and Bob Meet Banach

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

• 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

“[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