Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely positive maps on modules, instruments, extremality problems,
  and applications to physics   Convex sets of completely positive maps and positive semidefinite kernels are
considered in the most general context of modules over $C^*$-algebras and a
complete charaterization of their extreme points is obtained. As a byproduct,
we determine extreme quantum instruments, preparations, channels, and extreme
autocorrelation functions. Various applications to quantum information and
measurement theories are given. The structure of quantum instruments is
analyzed thoroughly.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio