= Quadrature noise ellipse
For a single-mode Gaussian state with no quadrature covariance, the covariance contour has semiaxes $\sqrt{\operatorname{Var}X}$ and $\sqrt{\operatorname{Var}P}$. A <coherent state> has both equal to $1/2$ in the convention $[X,P]=i/2$. A pure <squeezed vacuum state> has semiaxes $e^{-r}/2$ and $e^r/2$; the uncertainty area remains fixed while one noise width decreases. An ellipse of means alone does not specify a general non-Gaussian state.<Quantum Optical Communication lecture 6 by Jeffrey H. Shapiro>[Slides9–12, physical PDF pp.5–6: minimum-uncertainty and squeezed states]{ref}
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