Proposition: Interface separation

Among these three interfaces, only ${\mathcal{M}}_C$ removes $C$ from the returned quantum context. Moreover,

Coherent recording returns a quantum carrier and is not itself a classical recorded channel.

Proof. The assertions about returned names follow from the displayed domains and codomains. The partial-trace identity is Theorem thm:instrument. For a superposition of two clock basis states, coherent recording contains off-diagonal terms between the corresponding $C\otimes A$ states. Hence it is not generally block diagonal in $A$.