Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient condition for the reduced dynamics of an open
  quantum system interacting with an environment to be linear   The dynamics of a closed quantum system, under a unitary time evolution $U$,
is, obviously, linear. But, the reduced dynamics of an open quantum system $S$,
interacting with an environment $E$, is not linear, in general. Dominy et al.
[Quant. Inf. Process. 15, 465 (2016)] considered the case that the set
$\mathcal{S}=\lbrace\rho_{SE}\rbrace$, of possible initial states of the
system-environment, is convex and, also, possesses another property, which they
called $U$-consistency. They have shown that, under such circumstances, the
reduced dynamics of the system $S$ is linear. Whether the Dominy-Shabani-Lidar
framework is the most general one is the subject of this paper. We assume that
the reduced dynamics is linear and show that this leads us to their framework.
In other words, the reduced dynamics of the system is linear if and only if it
can be formulated within the Dominy-Shabani-Lidar framework.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph