Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous ensembles and the $\chi$-capacity of infinite-dimensional
  channels   The paper is devoted to systematic study of the $\chi$-capacity (underlying
the classical capacity) of infinite dimensional quantum channels. An essential
feature of this case is the natural appearance of the input constraints and
infinite, in general, ``continuous'' state ensembles, defined as probability
measures on the set of all quantum states. By using compactness criteria from
probability theory and operator theory it is shown that the set of all
generalized ensembles with the average (barycenter) in a compact set of states
is itself a compact subset of the set of all probability measures. With this in
hand we give a sufficient condition for the existence of an optimal generalized
ensemble for a constrained quantum channel. This condition can be verified in
the case of Bosonic Gaussian channels with constrained mean energy. The
importance of the above condition is shown by considering example of a
constrained channel with no optimal generalized ensemble. In the case of convex
constraints a characterization of the optimal generalized ensemble is obtained
extending the `` maximal distance'' property.

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs