Gheondea, A.2019-01-242019-01-2420102067-9009http://hdl.handle.net/11693/48319Motived 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.C∗-algebraCompletely positive mapTensor productStinespring representationKraus formChoi’s matrixRadonNikodym derivativeQuantum operationArticle