Definition: Complete emission interface

A complete finite emission interface consists of an input code ${\mathcal{H}}_C$, an accessible output ${\mathcal{H}}_R$, an inaccessible output ${\mathcal{H}}_K$, and an isometry

Every initially fixed auxiliary mixed state is purified, and its purification is assigned to the accessible or inaccessible output. The interface defines

The superscript $c$ refers to the complement of this specified dilation.