Preparation independence (${\mu }_{{\psi }_1,\dots ,{\psi }_n}={⨂}_i{\mu }_{{\psi }_i}$)

Independently operated quantum state preparations are assumed to produce independent underlying physical states. Their joint preparation measure factors into the single-system measures. This ontic factorization is an additional assumption, not a consequence of operational independence alone. It turns a common single-system overlap of mass $\epsilon$ into a common $n$-system overlap of mass ${\epsilon }^n$ in the PBR theorem.