Exact record and instrument criteria

Let $\{P_z\}$ be a finite projective resolution of $I_H$, let $q:Z\to W$ aggregate fine outcomes, and put

Let $T:\mathcal{B}(H)\to \mathcal{B}(K)$ be a channel and $\{{\mathcal{I}}_w{\}}_{w\in W}$ an instrument on $K$, with $E_w={\mathcal{I}}_w^{\ast }(I_K)$. Compare

This comparison uses represented fine projections on a common input space. For a genuinely destructive protocol, any subsequent removal or identification of $S$ must be included explicitly in $T$; it is not hidden in ${\Delta }_w$.