Browsing by Subject "Stinespring representation"

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    Complete positivity in operator algebras
    (2006) Kavruk, Ali Şamil
    In this thesis we survey positive and completely positive maps defined on operator systems. In Chapter 3 we study the properties of positive maps as well as construction of positive maps under certain conditions. In Chapter 4 we focus on completely positive maps. We give some conditions on domain and range under which positivity implies complete positivity. The last chapter consists of Stinespring’s dilation theorem and its applications to various areas.
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    The three equivalent forms of completely positive maps on matrices
    (Editura Universitatea din Bucuresti, 2010) Gheondea, A.
    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.