Questions tagged [gaussian-states]

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5
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Why is a state Gaussian if and only if its covariance matrix satisfies $\boldsymbol\sigma+i\boldsymbol\Omega\ge0$?

Let $\rho$ be a Gaussian state, described by the $2N\times 2N$ covariance matrix $\newcommand{\bs}[1]{{\boldsymbol{#1}}}\bs\sigma$. Denote with $\bs\Omega$ the $N$-mode symplectic form associated with ...
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How to write the covariance matrix of a quantum gaussian state as a function of photon numbers?

Assume having a one-mode quantum Gaussian state with quadrature observable vector $\hat r = [\hat q , \hat p ] $ and covariance matrix $\sigma$. According to definition [1]: \begin{equation} \sigma = \...