Example: The mean-only stop

The density $\frac{1}{2}|0⟩⟨0|+\frac{1}{2}|2⟩⟨2|$ is centered and gauge-invariant, has $⟨{b_h}^2⟩=0$, and has mean one. It is not the geometric state with mean one. Quasifreeness is essential to Theorem thm:marginal.