Preparation and the comparison interface

Let $M\cong {\mathbb{C}}^D$ be the logical payload space. At every site use the same declared computational basis and the same blank state

For a realization $X$, the encoding channel is

All auxiliary registers are prepared before time zero, independently of the payload and of any reference. Transport time is measured from availability of this primed finite network and the source payload. Preparation time and physical apparatus construction are not included in the transport-time estimate.

For a destination $b\in X$, define

followed by the fixed basis identification $A_b\cong M$. This is an output-reduction convention, not a physical command that transports discarded systems to the destination.

The logical channel of a realization is

Thus the physical interface may grow with $j$, while the comparison interface $M$ remains fixed.