Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Common Parametrization for Finite Mode Gaussian States, their
  Symmetries and associated Contractions with some Applications   Let $\Gamma(\mathcal{H})$ be the boson Fock space over a finite dimensional
Hilbert space $\mathcal{H}$. It is shown that every gaussian symmetry admits a
Klauder-Bargmann integral representation in terms of coherent states.
Furthermore, gaussian symmetries, gaussian states and second quantization
contractions, all of these operators belong to a weakly closed, selfadjoint
semigroup $\mathcal{E}_2(\mathcal{H})$ of bounded operators in
$\Gamma(\mathcal{H})$. This yields, a new parametrization of gaussian states,
which is a very fruitful alternative to the customary parametrization by
position-momentum mean vectors and covariance matrices. This leads to a rich
harvest of corollaries:
  (i) every gaussian state $\rho$ admits a factorization $\rho =
Z_{1}^{\dagger}Z_{1}$, where $Z_{1}$ is an element of
$\mathcal{E}_2(\mathcal{H})$ and has the form $Z_{1} =
\sqrt{c}\Gamma(\sqrt{\Lambda})\exp{\sum_{r=1}^{n} \lambda_ra_r+\sum_{r,s=1}^{n}
\alpha_{rs}a_{r}a_{s}}$ on the dense linear manifold generated by all
exponential vectors, $\Lambda$ being a positive operator in $\mathcal{H}$,
$a_{r}, 1\leq r \leq n$ are the annihilation operators corresponding to the $n$
different modes in $\Gamma(\mathcal{H})$, $\lambda_r\in \mathbb{C}$ and
$[\alpha_{rs}]$ is a symmetric matrix in $M_n(\mathbb{C})$;
  (ii) an explicit particle basis expansion of an arbitrary mean zero pure
gaussian state vector along with a density matrix formula for a general
gaussian state in terms of its $\mathcal{E}_2(\mathcal{H})$-parameters;
  (iii) an easy test for the entanglement of pure gaussian states and a class
of examples of pure $n$-mode gaussian states which are completely entangled;
  (iv) tomography of an unknown gaussian state in $\Gamma(\mathbb{C}^n)$ by the
estimation of its $\mathcal{E}_2(\mathbb{C}^n)$-parameters using $O(n^2)$
measurements with a finite number of outcomes.

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The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci