Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology of the cone of positive maps on qubit systems   An alternative, geometrical proof of a known theorem concerning the
decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has
been presented. The premise of the proof is the identification of positive maps
with operators preserving the Lorentz cone in four dimensions, and it allows to
decompose the positive maps with respect to those preserving the boundary of
the cone. In addition, useful conditions implying complete positivity of a map
of $M_{2}(\mathbb{C})$ have been given, together with a sufficient condition
for complete positivity of an extremal Schwarz map of $M_{n}(\mathbb{C})$.
Lastly, following the same geometrical approach, a description in topological
terms of maps that are simultaneously completely positive and completely
copositive has been presented.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org