Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extreme points of the set of density matrices with positive partial
  transpose   We present a necessary and sufficient condition for a finite dimensional
density matrix to be an extreme point of the convex set of density matrices
with positive partial transpose with respect to a subsystem. We also give an
algorithm for finding such extreme points and illustrate this by some examples.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom