Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting multimode entanglement by symplectic uncertainty relations   A hierarchy of multimode uncertainty relations on the second moments of n
pairs of canonical operators is derived in terms of quantities invariant under
linear canonical (i.e. symplectic) transformations. Conditions for the
separability of multimode continuous variable states are derived from the
uncertainty relations, generalizing the inequalities obtained in [Phys. Rev.
Lett. 96, 110402 (2006)] to states with some transposed symplectic eigenvalues
equal to 1. Finally, to illustrate the methodology proposed for the detection
of continuous variable entanglement, the separability of multimode noisy
GHZ-like states is analysed in detail with the presented techniques, deriving a
necessary and sufficient condition for the separability of such states under an
`even' bipartition of the modes.

11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc