# Tag Info

Accepted

• 6,957

### What is the complementary map of a serial concatenation of quantum channels?

The formula has multiple problems: first, complementary channels are of course not unique and, even worse, the output dimension is not fixed; so to make things rigorous we would have to impose some ...
• 2,001

### What is the domain of the dual map of a quantum channel?

The key here is linearity; a (real-)linear map $\Phi$ defined on all self-adjoint bounded operators on $H$ has a unique extension to all of $B(H)$. This is due to the fact that every $B\in B(H)$ can ...
• 2,001
1 vote
Accepted

### Are peripheral eigenvalues of a completely positive map always semisimple?

Consider $$K:=\begin{pmatrix}1&1\\0&1\end{pmatrix}$$ as well as $\Phi:=K(\cdot)K^\dagger$. This map is completely positive (because $\Phi$ is in Kraus form) and even strictly positive ...
• 2,001
1 vote

I'm interpreting this as a notation question for $\mathcal{N}$ restricted to act on $\{I, Z\}$. One notation I like is to write $\mathbf{Z}^{\mathbf{b}}:= \bigotimes_{i=1}^k Z_i^{b_i}$, where $\mathbf{... • 7,183 1 vote Accepted ### Are Stinespring unitaries that give rise to the same channel locally unitarily equivalent? As it turns out the statement in question is wrong. For a counterexample consider the full-rank environment state$\$ \omega=\begin{pmatrix} \frac12&0&0\\0&\frac14&0\\0&0&\...
• 2,001

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