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- W3136858928 abstract "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 $mathcal{H}$, $a_{r}, 1leq r leq n$ are the annihilation operators corresponding to the $n$ different modes in $Gamma(mathcal{H})$, $lambda_rin mathbb{C}$ 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." @default.
- W3136858928 created "2021-03-29" @default.
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- W3136858928 date "2021-02-01" @default.
- W3136858928 modified "2023-09-27" @default.
- W3136858928 title "A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications" @default.
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- W3136858928 doi "https://doi.org/10.1063/5.0019413" @default.
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