Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Merging of positive maps: a construction of various classes of positive
  maps on matrix algebras   For two positive maps $\phi_i:B(\mathcal{K}_i)\to B(\mathcal{H}_i)$, $i=1,2$,
we construct a new linear map $\phi:B(\mathcal{H})\to B(\mathcal{K})$, where
$\mathcal{K}=\mathcal{K}_1\oplus\mathcal{K}_2\oplus\mathbb{C}$,
$\mathcal{H}=\mathcal{H}_1\oplus\mathcal{H}_2\oplus\mathbb{C}$, by means of
some additional ingredients such as operators and functionals. We call it a
merging of maps $\phi_1$ and $\phi_2$. We discuss properties of this
construction. In particular, we provide conditions for positivity of $\phi$, as
well as for $2$-positivity, complete positivity and nondecomposability. In
particular, we show that for a pair composed of $2$-positive and $2$-copositive
maps, there is a nondecomposable merging of them. One of our main results
asserts, that for a canonical merging of a pair composed of completely positive
and completely copositive extremal maps, their canonical merging is an exposed
positive map. This result provides a wide class of new examples of exposed
positive maps. As an application, new examples of entangled PPT states are
described.

23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org