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An Ergodic Dilation of Completely Positive Maps
Ergodic Dilation Completely Positive Maps Operator Algebras
2011/9/15
Abstract: We shall prove the following Stinespring-type theorem: there exists a triple $(\pi,\mathcal{H},\mathbf{V})$ associated with an unital completely positive map $\Phi:\mathfrak{A}\rightarrow \m...
Three commuting, unital, completely positive maps that have no minimal dilation
Product system subproduct system semigroups of completely positive maps
2011/1/20
In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann a...
Interpolation problems by completely positive maps
Completely positive map quantum operations dilations Hermitian matrices
2011/1/19
Given commuting families of Hermitian matrices {A1, . . . ,Ak} and {B1, . . . ,Bk},conditions for the existence of a completely positive map Φ, such that Φ(Aj) = Bj for j =1, . . . , k, are studied. A...
Normal completely positive maps on the space of quantum operations
Completely positive and completely bounded maps Dilation theorems Stinespring representation
2011/2/21
We define a class of higher-order linear maps that transform quantum operations into quantum operations and satisfy suitable requirements of normality and complete positivity. For this class of maps w...
Factorization and dilation problems for completely positive maps on von Neumann algebras
Factorization dilation problems for completely positive maps von Neumann algebras
2010/11/29
We study factorization and dilation properties of Markov maps between von Neumann algebras
equipped with normal faithful states, i.e., completely positive unital maps which preserve the
given states...