**Mathematical Surveys and Monographs**

Volume: 223;
2017;
Hardcover

MSC: Primary 46; 52; 81; 60;

Print ISBN: 978-1-4704-3468-7

Product Code: SURV/223

List Price: $116.00

Individual Member Price: $92.80

**Electronic ISBN: 978-1-4704-4172-2
Product Code: SURV/223.E**

List Price: $116.00

Individual Member Price: $92.80

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# Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory

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*Guillaume Aubrun; Stanisław J. Szarek*

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.

This book 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. We have tried to make the book as user-friendly as possible,
with numerous tables, explicit estimates, and reasonable constants
when possible, so as to make it a useful reference even for
established mathematicians generally familiar with the
subject.

#### Readership

Graduate students and researchers interested in mathematical aspects of quantum information theory and quantum computing.