The three equivalent forms of completely positive maps on matrices
Annals of the University of Bucharest (Mathematical Series)
Editura Universitatea din Bucuresti
79 - 98
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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.
Completely positive map