Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive finite rank elementary operators and characterizing
  entanglement of states   In this paper, a class of indecomposable positive finite rank elementary
operators of order $(n,n)$ are constructed. This allows us to give a simple
necessary and sufficient criterion for separability of pure states in bipartite
systems of any dimension in terms of positive elementary operators of order
$(2,2)$ and get some new mixed entangled states that can not be detected by the
positive partial transpose (PPT) criterion and the realignment criterion.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con