The Functional Analysis of Quantum Information Theory

TL;DR

This compilation summarizes a workshop on the mathematical framework of quantized functional analysis and its applications to quantum communication, focusing on operator spaces, entanglement, and operator methods.

Contribution

It introduces the mathematical tools of quantized functional analysis applied to quantum information theory, highlighting recent developments and applications.

Findings

Operator spaces and completely bounded maps are crucial in quantum communication.

Schmidt number and rank are key in characterizing entangled states.

Operator methods provide new insights into quantum information problems.

Abstract

This book is a compilation of notes from a two-week international workshop on the "The Functional Analysis of Quantum Information Theory" that was held at the Institute of Mathematical Sciences during 26/12/2011-06/01/2012. The workshop was devoted to the mathematical framework of quantized functional analysis (QFA), and aimed at illustrating its applications to problems in quantum communication. The lectures were given by Gilles Pisier (Pierre and Marie Curie University and Texas A&M), K.R. Parthasarathy (ISI Delhi), Vern Paulsen (University of Houston), and Andreas Winter (Universitat Autonoma de Barcelona). Topics discussed include Operator Spaces and Completely bounded maps, Schmidt number and Schmidt rank of bipartite entangled states, Operator Systems and Completely Positive Maps, and, Operator Methods in Quantum Information.