Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of time-covariant operations on quantum systems with
  continuous and/or discrete energy spectrum   Every completely positive map G that commutes which the Hamiltonian time
evolution is an integral or sum over (densely defined) CP-maps G_\sigma where
\sigma is the energy that is transferred to or taken from the environment. If
the spectrum is non-degenerated each G_\sigma is a dephasing channel followed
by an energy shift. The dephasing is given by the Hadamard product of the
density operator with a (formally defined) positive operator. The Kraus
operator of the energy shift is a partial isometry which defines a translation
on R with respect to a non-translation-invariant measure.
  As an example, I calculate this decomposition explicitly for the rotation
invariant gaussian channel on a single mode.
  I address the question under what conditions a covariant channel destroys
superpositions between mutually orthogonal states on the same orbit. For
channels which allow mutually orthogonal output states on the same orbit, a
lower bound on the quantum capacity is derived using the Fourier transform of
the CP-map-valued measure (G_\sigma).

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs