Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separable states can be used to distribute entanglement   We show that no entanglement is necessary to distribute entanglement; that
is, two distant particles can be entangled by sending a third particle that is
never entangled with the other two. Similarly, two particles can become
entangled by continuous interaction with a highly mixed mediating particle that
never itself becomes entangled. We also consider analogous properties of
completely positive maps, in which the composition of two separable maps can
create entanglement.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg