Destructive Enter and coherent recording

For a measured register $S$ and a surviving register $T$, set $M_x=⟨x{|}_S\otimes I_T$. Destructive computational readout is

The measured names in $S$ are consumed; $K$ is classical. The surviving quantum output is $T$, not a renamed copy of $S$. This is the readout accounting used in CheungI,CheungEn03,CheungEn04,CheungHawk04B.