All Questions

The only example I know of a positive map which is not completely positive is the transpose map on $M_n(\mathbb{C})$. Of course, one can come up with minor perturbations of this (compose it with, or ...

Consider the complex $n$-by-$n$ matrices $M_n$. Suppose that $A_i$, for $i=1,\ldots,n^2$, satisfy $\mathrm{Tr}(A_i^* A_j)=\delta_{ij}$, so that together they form an orthonormal basis for $M_n$. ...

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 ...