Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Standard forms and entanglement engineering of multimode Gaussian states
  under local operations   We investigate the action of local unitary operations on multimode (pure or
mixed) Gaussian states and single out the minimal number of locally invariant
parametres which completely characterise the covariance matrix of such states.
For pure Gaussian states, central resources for continuous-variable quantum
information, we investigate separately the parametre reduction due to the
additional constraint of global purity, and the one following by the
local-unitary freedom. Counting arguments and insights from the phase-space
Schmidt decomposition and in general from the framework of symplectic analysis,
accompany our description of the standard form of pure n-mode Gaussian states.
In particular we clarify why only in pure states with n<=3 modes all the direct
correlations between position and momentum operators can be set to zero by
local unitary operations. For any n, the emerging minimal set of parametres
contains complete information about all forms of entanglement in the
corresponding states. An efficient state engineering scheme (able to encode
direct correlations between position and momentum operators as well) is
proposed to produce entangled multimode Gaussian resources, its number of
optical elements matching the minimal number of locally invariant degrees of
freedom of general pure n-mode Gaussian states. We demonstrate that so-called
"block-diagonal" Gaussian states, without direct correlations between position
and momentum, are systematically less entangled, on average, than arbitrary
pure Gaussian states.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc