num_pages: 413
description: 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 at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT especially the part 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.
language: English
title: Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory
publisher: American Mathematical Society