Questions tagged [complete-positivity]
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7 questions with no upvoted or accepted answers
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"Dual" of a CP map
Let $M,N$ be von Neumann algebras, and let $\phi:M\rightarrow N$ be a normal completely positive map. I am interested in conditions when there is a "dual" normal completely positive map $\...
- 18.7k
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Does the Cauchy–Schwarz inequality imply 2-positivity?
Recall the following generalisation of Cauchy–Schwarz.
Theorem. Let $f\colon \mathscr{A} \to \mathscr{B}$ be a linear 2-positive map between C$^*$-algebras. Then for all $a,b \in \mathscr{A}$ we ...
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Extensions of completely positive mappings
I would like to ask the following two questions.
Let $1_{\mathcal{H}}\in \mathcal{A}\subset\mathcal{B}\subset\overline{\mathcal{A}}^{SOT}\subset\mathbb{B}(\mathcal{H})$ be a sequence of $C^{\ast}$-...
- 619
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Tight upper bound for $m[Q^k - Q^{k+1}]$ for completely positive linear maps
Let $m: \mathcal{L}(\mathbb{R}^{d \times d}) \to \mathbb{R}$ be the function
$$
m[H] = \frac{\lambda_{\max}(H[\mathbf{I}])}{\lambda_{\max}(H)},
$$
where $\lambda_{\max}$ denotes the largest eigenvalue....
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Stinespring's theorem: can we choose the dilation to be an isometry?
Let $A$ be a $C^*$-algebra and $\varphi: A \to B(H)$ be a completely positive contractive map. Stinespring's theorem says that there exists a $*$-representation $\pi: A \to B(H')$ and a bounded ...
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Completely positive, unital maps acting on unitary operators [solved]
Call a completely positive, irreducible, unital map $E$ on the operators on a finite-dimensional Hilbert-space primitive if there is only a single eigenvalue with modulus 1 (all others have modulus &...
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Example of a unital contractive map that is not completely positive on an operator system
I am aware of maps that are positive but not completely positive (for example transpose map). BUT I can not think of an example of the following type.
Does there exist an operator $T$ such that a map $...
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