Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distillability and PPT entanglement of low-rank quantum states   It is known that he bipartite quantum states, with rank strictly smaller than
the maximum of the ranks of its two reduced states, are distillable by local
operations and classical communication. Our first main result is that this is
also true for NPT states with rank equal to this maximum. (A state is PPT if
the partial transpose of its density matrix is positive semidefinite, and
otherwise it is NPT.) This was conjectured first in 1999 in the special case
when the two local ranks are equal. Our second main result provides a complete
solution of the separability problem for bipartite states of rank 4. Namely, we
show that such a state is separable if and only if it is PPT and its range
contains at least one product state. We also prove that the so called
checkerboard states are distillable if and only if they are NPT.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex