Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory
About this Title
Guillaume Aubrun, Université Claude Bernard Lyon 1, Villeurbanne, France and Stanisław J. Szarek, Case Western Reserve University, Cleveland, OH
Publication: Mathematical Surveys and Monographs
Publication Year:
2017; Volume 223
ISBNs: 978-1-4704-3468-7 (print); 978-1-4704-4172-2 (online)
DOI: https://doi.org/10.1090/surv/223
MathSciNet review: MR3699754
MSC: Primary 46-02; Secondary 46B20, 52A07, 81-02, 81P45, 81R50, 94-02, 94A17
Table of Contents
Front/Back Matter
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 Santaló point via duality of cones
- Hints to exercises
- Notation