The three equivalent forms of completely positive maps on matrices

Date
2010
Authors
Gheondea, A.
Advisor
Instructor
Source Title
Annals of the University of Bucharest (Mathematical Series)
Print ISSN
2067-9009
Electronic ISSN
Publisher
Editura Universitatea din Bucuresti
Volume
1 (LIX)
Issue
1
Pages
79 - 98
Language
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Motived by the importance of quantum operations in quantum information theory, we rigorously present the three equivalent (Stinespring, Kraus, and Choi) forms of completely positive maps on full C∗-algebras of matrices, as well as their connection with the Arveson’s Radon-Nikodym derivative. In order to make this accessible to a broader audience we employ mostly linear algebra facts and carefully review the prerequisites.

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Other identifiers
Book Title
Keywords
C∗-algebra, Completely positive map, Tensor product, Stinespring representation, Kraus form, Choi’s matrix, RadonNikodym derivative, Quantum operation
Citation
Published Version (Please cite this version)