Phase-dependent cat-state quadrature variance ($\mathrm{Var}{X}_2=\frac{1}{4}-\frac{{\alpha }^{2}s(\cos \varphi +s)}{(1+s\cos \varphi {)}^2}$)

For real $\alpha$, put $s=e^{-2{\alpha }^2}$ in $N(|\alpha ⟩+e^{i\varphi }|-\alpha ⟩)$. Its mean second quadrature is $-\alpha s\sin \varphi /(1+s\cos \varphi )$, which is generally nonzero. Subtracting its square from the second moment gives the displayed variance and squeezing precisely when $\cos \varphi >-s$, for nonzero finite amplitude. A useful counterexample to confusing moment and variance is $\varphi =\pi /2$.