Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Faces of the set of Quantum Channels   A linear map $L$ from ${\mathbb C}^{n \times n}$ into ${\mathbb C}^{n \times
n}$ is called a quantum channel if it is completely positive and trace
preserving. The set ${\cal L}_n$ of all such quantum channels is known to be a
compact convex set. While the extreme points of ${\cal L}_n$ can be
characterized, not much is known about the structure of its higher dimensional
faces. Using the so called Choi matrix $Z(L)$ associated with the quantum
channel $L$, we compute the maximum dimension of a proper face of ${\cal L}_n$,
and in addition the possible dimensions of faces generated by $L$ when $rank \
Z(L)=2 $.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics