Proposition: Whole-block coherent access

With a zero receiver register, the two-cell transfer leaves the same all-vacuum cell state for every basis input and induces

It preserves every input coherence and every external reference.

Proof. The final cell factor is $|g⟩$ for every input basis vector. Linearity gives a common cell environment for every superposition. Tracing that common environment leaves the stated isometric channel, including referenced inputs.