Description
Book SynopsisTrade Review[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 ReviewsTable of Contents
- Alice and Bob: Mathematical Aspects of Quantum Information: Notation and basic concepts
- Elementary convex analysis
- The mathematics of quantum information theory
- Quantum mechanics for mathematicians
- Banach and His spaces: Asymptotic Geometric Analysis Miscellany: More convexity
- Metric entropy and concentration of measure in classical spaces
- Gaussian processes and random matrices
- Some tools from asymptotic geometric analysis
- The Meeting: AGA and QIT: Entanglement of pure states in high dimensions
- Geometry of the set of mixed states
- Random quantum states
- Bell inequalities and the Grothendieck-Tsirelson inequality
- POVMs and the distillability problem
- Gaussian measures and Gaussian variables
- Classical groups and manifolds
- Extreme maps between Lorentz cones and the $S$-lemma
- Polarity and the Santalo point via duality of cones
- Hints to exercises
- Bibliography
- Notation
- Index.
