The Clifford benchmark and its inherited unlocking state

Every proper even-family subset is constant. The only nonconstant proper odd-family subsets are $\{2,3\}$ and $\{1,3\}$, carrying $X$ and $Z$, respectively. For example, the former is $\rho \mapsto (I-x{X}_2{Z}_3)/4$, an entanglement-breaking measure-and-prepare channel. Both chronological prefixes $\{1\}$, $\{1,2\}$ are constant. Applying $U{F}^L$ and discarding positions $1,3$ recovers the message from the full triple.

For even parity, the normalized Bell-input state is