An exactly solved flagged-erasure benchmark

This section supplies analytic benchmark results rather than unexecuted numerical claims.

Fix a declared access region $A$ of size $m$. Each qubit in $A$ is independently transmitted with probability $q$, otherwise replaced by an orthogonal erasure flag. Flags reveal the surviving subset $S\subseteq A$, and are independent of the logical input. The inaccessible $\bar{A}$ is traced out. The complete accessible channel is the direct sum

On $|S|\ge 3$, apply the decoder from Theorem thm:idealaccess. On $|S|\le 2$, return $I_2/2$. All flags and branches are accounted for.