Title: Alice and Bob meet Banach : the interface of asymptotic geometric analysis and quantum information theory /
Authors: Aubrun, Guillaume, 1981-; Szarek, Stanisław J.,
Year: 2017
Subjects: Geometric analysis.; Quantum theory; Functional analysis Normed linear spaces and Banach spaces; Banach lattices Normed linear spaces and Banach spaces; Banach lattices.; Convex and discrete geometry General convexity General convexity.; Quantum theory Axiomatics, foundations, philosophy Axiomatics, foundations, philosophy.; Functional analysis Normed linear spaces and Banach spaces; Banach lattices Local theory of Banach spaces.; Functional analysis Normed linear spaces and Banach spaces; Banach lattices Probabilistic methods in Banach space theory.; Convex and discrete geometry Discrete geometry Packing and covering in $n$ dimensions.; Probability theory and stochastic processes Probability theory on algebraic and topological structures Random matrices (probabilistic aspects; for algebraic aspects see 15B52); Quantum theory Axiomatics, foundations, philosophy Quantum coherence, entanglement, quantum correlations.; Geometric analysis; Quantum theory
Abstract: 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 geo.
Contents: Part 1. Alice and Bob : mathematical aspects of quantum information theory -- Part 2. Banach and his spaces : asymptotic geometric analysis miscellany -- Part 3. The meeting : AGA and QIT.