Recorded circuits and the two statistical models

All Hilbert spaces are finite-dimensional. A state is a positive operator of trace one. An effect is an operator $0\le M\le 1$. We use

A finite qubit set $Q$ has Hilbert space ${\mathcal{H}}_Q={⨂}_{q\in Q}{\mathbb{C}}^2$. For $S\subseteq Q$, write $\overline{S}=Q\setminus S$.