Optional terminal observation

A prescribed terminal measurement may be appended after quantum return:

Cout := BasisUnitary(Cout); x := Enter(Cout); returnBit(x);

Its target is the measurement channel $\mathcal{M}$, not ${\mathrm{id}}_C$. By contraction,

The converse for one chosen measurement fails: computational dephasing preserves its computational record but not off-diagonal matrix units.

Enter is not a magic evaluator. A program may be mathematically analysed for nonstabilizerness, but the primitive semantics of $\mathsf{Enter}$ is the instrument (eq:enter).