Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Alberti-Uhlmann Condition for Unital Channels   We address the problem of existence of completely positive trace preserving
(CPTP) maps between two sets of density matrices. We refine the result of
Alberti and Uhlmann and derive a necessary and sufficient condition for the
existence of a unital channel between two pairs of qubit states which
ultimately boils down to three simple inequalities.

14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci