Objects and the three ledgers

All channel results through Section sec:examples are finite dimensional. The modular module has a different ambient algebra and is introduced separately.

Let $C\cong {\mathbb{C}}^d$, $d\ge 2$, be a logical input. Let $A$ be the accessible output and $B$ the complete complement. A declared complete isometry is

Define

If the physical preparation includes a mixed ancillary state, its purifier is included in $B$. Discarded flags, unavailable modes, and unreturned quantum outputs are included according to the declared dilation.

A decoder is a completely positive trace-preserving map, abbreviated CPTP,

The returned quantum channel is $\mathcal{E}=\mathcal{DN}$. A destructive validation analyzer acts afterward and is not included in the returned quantum task.