Quadrature noise ellipse

For a single-mode Gaussian state with no quadrature covariance, the covariance contour has semiaxes $\sqrt{\mathrm{Var}X}$ and $\sqrt{\mathrm{Var}P}$. 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.^[ref]