Logical comparison maps

For a realization, let $E_n$ place the external logical inputs into their designated physical slots and append the common prepared background. Let $D_n$ restrict the final physical output to the designated logical output slots and complete records, then apply their fixed type identifications.

Both maps are CPTP. They are not physical nonlocal transport operations: they are comparison maps identifying specified external interfaces.

If an interface is padded into a larger reserved space, choose a CPTP decoder that inverts the padding on its code subspace and sends the complementary weight to a fixed admitted output state. Thus padding has a complete deterministic extension. The comparison is

Convergence means half-diamond convergence of these maps. It includes every untouched reference and implies total-variation convergence of every fixed complete finite readout.

convention. One may reserve interfaces separately for each finite experiment, as in En05-A. Alternatively, fix in advance a number of slots and a slot dimension tending to infinity with $n$. Every fixed finite skeleton then fits on all sufficiently fine scales. The substrate and partition schedule do not depend on its input state or its local instrument choices.