Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entangled symmetric states of N qubits with all positive partial
  transpositions   From both theoretical and experimental points of view symmetric states
constitute an important class of multipartite states. Still, entanglement
properties of these states, in particular those with positive partial
transposition (PPT), lack a systematic study. Aiming at filling in this gap, we
have recently affirmatively answered the open question of existence of
four-qubit entangled symmetric states with positive partial transposition and
thoroughly characterized entanglement properties of such states [J. Tura et
al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we
continue on characterizing PPT entangled symmetric states. On the one hand, we
present all the results of our previous work in a detailed way. On the other
hand, we generalize them to systems consisting of arbitrary number of qubits.
In particular, we provide criteria for separability of such states formulated
in terms of their ranks. Interestingly, for most of the cases, the symmetric
states are either separable or typically separable. Then, edge states in these
systems are studied, showing in particular that to characterize generic PPT
entangled states with four and five qubits, it is enough to study only those
that assume few (respectively, two and three) specific configurations of ranks.
Finally, we numerically search for extremal PPT entangled states in such
systems consisting of up to 23 qubits. One can clearly notice regularity behind
the ranks of such extremal states, and, in particular, for systems composed of
odd number of qubits we find a single configuration of ranks for which there
are extremal states.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess