Definition: Finite code and complete output

A finite evaporation interface consists of:

1. a code space ${\mathcal{H}}_C$ of dimension $d<\infty$;

2. an accessible output ${\mathcal{H}}_A$;

3. a residual output ${\mathcal{H}}_B$;

4. an isometry

   $$W:{\mathcal{H}}_C⟶{\mathcal{H}}_A\otimes {\mathcal{H}}_B.$$

All initial auxiliary states are fixed independently of the code. Every mixed auxiliary is purified, and its purifier is included in $A$ or $B$. The corresponding channels are

An arbitrary reference $Q$ is left untouched.