Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond the standard entropic inequalities: stronger scalar separability
  criteria and their applications   Recently it was shown that if a given state fulfils the reduction criterion
it must also satisfy the known entropic inequalities. Now the questions arises
whether on the assumption that stronger criteria based on positive but not
completely positive maps are satisfied, it is possible to derive some scalar
inequalities stronger than the entropic ones. In this paper we show that under
some assumptions the extended reduction criterion [H.-P. Breuer, Phys. Rev.
Lett 97, 080501 (2006); W. Hall, J. Phys. A 40, 6183 (2007)] leads to some
entropic--like inequalities which are much stronger than their entropic
counterparts. The comparison of the derived inequalities with other
separability criteria shows that such approach might lead to strong scalar
criteria detecting both distillable and bound entanglement. In particular, in
the case of SO(3)-invariant states it is shown that the present inequalities
detect entanglement in regions in which entanglement witnesses based on
extended reduction map fail. It should be also emphasized that in the case of
$2\otimes N$ states the derived inequalities detect entanglement efficiently,
while the extended reduction maps are useless when acting on the qubit
subsystem. Moreover, there is a natural way to construct a many-copy
entanglement witnesses based on the derived inequalities so, in principle,
there is a possibility of experimental realization. Some open problems and
possibilities for further studies are outlined.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph