Example: Vacuous determinacy

Take $\mathfrak{M}=M_2$, $\mathfrak{A}=\mathbb{C}1$, and ${\mathcal{S}}_{\mathrm{adm}}=\{{\omega }_0\}$. The identity channel passes every equal-snapshot test on this preparation class, but

All-state quantification, or an explicit fiber-separation condition, is therefore essential.