Browsing by Subject "Completely positive map"

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    Dilations of some VH-spaces operator valued invariant Kernels
    (Springer, 2012) Gheondea, A.
    We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of *-semigroups from the point of view of generation of *-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifies many dilation results, in particular B. Sz.-Nagy's and Stinesprings' dilation type theorems. © 2012 Springer Basel.
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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.