Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A SURVEY OF COMPLETELY BOUNDED MAPS

Vern I. Paulsen

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

These notes are an expanded version of my talk at the con- ference on Operator Structures in Quantum Information Theory at the Ban International Research Station on February 13, 2007. They are intended to give an introduction to some of the topics in the theory of operator spaces and completely bounded maps that might be useful for researchers in quantum information theory

Related papers

A QUANTIZATION PROCEDURE BASED ON COMPLETELY POSITIVE MAPS AND MARKOV OPERATORS

Carlos F. Lardizabal

We describe $ω$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other. Motivated by these facts, we describe a quantization procedure based on CP maps which are induced by Markov (transfer) operators. Classical dynamics are described by an action over essentially bounded functions. A non-expansive linear map, which depends on a choice of a probability measure, is the centerpiece connecting phenomena over function and matrix spaces.

•Aug 16, 2016•2 citations

Undecidability and incompleteness in quantum information theory and operator algebras

Isaac Goldbring

arXiv:2409.08342•Monatshefte für Mathematik•May 8, 2025•0 citations

The Functional Analysis of Quantum Information Theory

Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder

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.

arXiv:1410.7188•Oct 27, 2014•1 citation

Introduction to Special Issue: Operator Algebras and Quantum Information Theory

Yasuyuki Kawahigashi, David Pérez García, Mary Beth Ruskai

Journal of Mathematical Physics•Jan 1, 2016•0 citations

Quantum Information Theory -- Lecture Notes

Christoph Dittel

These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these disciplines, with the aim of providing you with an overview and a basic introduction. The corresponding lecture series is available on my YouTube channel.

arXiv:2311.12442•Nov 21, 2023•0 citations

Entropy of Completely Positive Maps and Applications to Quantum Information Theory

Ichiro Fujimoto

Trends in mathematics•Jan 1, 2016•0 citations
These notes are an expanded version of my talk at the con- ference on Operator Structures in Quantum Information Theory at the Ban International Research Station on February 13, 2007. They are intended to give an introduction to some of the topics in the theory of operator spaces and completely bounded maps that might be useful for researchers in quantum information theory
We describe ωωω-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other. Motivated by these facts, we describe a quantization procedure based on CP maps which are induced by Markov (transfer) operators. Classical dynamics are described by an action over essentially bounded functions. A non-expansive linear map, which depends on a choice of a probability measure, is the centerpiece connecting phenomena over function and matrix spaces.
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.