# Questions tagged [complete-positivity]

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### Completely positive maps on Coxeter groups - the general case

In the reference below Bozejko and Speicher showed the following (for the full statement see the remark on page 9): Let $(W,S)$ be a Coxeter system, let $\mathcal{H}$ be a Hilbert space and denote ...
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### Can the intersection of a unitary and an irreducibly represented injective $C^*$-algebra be $\{0\}$?

Let $\mathcal{A}$ be an injective $C^*$-algebra irreducibly acting on a Hilbert space $\mathcal{H}$, and let $\phi$ be a completely positive idempotent from $\mathbb{B}(\mathcal{H})$ onto $\mathcal{A}$...
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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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### Complete positivity with infinite dimensional auxillary spaces

The usual definition of complete positivity (e.g. Stinespring (1955), or Holevo's Statistical Structure of Quantum Theory) is that a linear map between (sub $C^*$ algebras of) the bounded operators on ...
• 133
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### Maps which are both completely positive and positive

Definition:A linear map $f:\mathbb C^n\to \mathbb C^n$ is called positive if $\langle fa,a\rangle\ge0$ for all $a\in \mathbb C^n$. Equivalently, $f\in M_{n}(\mathbb C)$ is positive if it can be ...
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### Reference on completely positive maps which are isometries

Let $\Phi:\mathcal{L}(H)\rightarrow \mathcal{L}(K)$ be a completely positive map sending positive self-adoint operators on a finite-dimensional Hilbert space $H$ to positive self-adoint operators on a ...
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### Completely Positive Maps and their dual in Separable Hilbert Space

Consider a separable Hilbert space $\mathcal{H}$, we can first define $T(\mathcal{H})$ the trace class of $\mathcal{H}$, then $D(\mathcal{H})$ to denote the set of positive operator with trace less ...
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### Bounded operators on the Stinespring representation space

Let $A$ be a $C^*$-algebra and let $\phi:A\to B(H)$ be a completely positive map. The Stinespring representation theorem constructs a representation of $A$ on a Hilbert space $K$, which is constructed ...
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