Manuscript En07-B@1 · En07-B.tex · definition · 45dff4a1

Definition: Complete code interface

The fixed finite interface · lines 204–219

En07-B@1#def:interface

Let $C, R, B$ be finite-dimensional Hilbert spaces and let $d = dim C \geq 2$ . A complete code interface is an isometry

V : C ⟶ R \otimes B, V^{†} V = I_{C} .

Its complete, accessible, and complementary channels are

V (X) = V X V^{†}, N (X) = Tr_{B} (V X V^{†}), E (X) = Tr_{R} (V X V^{†}) .

The designation $R$ is the declared accessible output; $B$ is its complete inaccessible complement.

Displayed formulas in this passage

unlabeled · line 208
$V : C ⟶ R \otimes B, V^{†} V = I_{C} .$
unlabeled · line 212
$V (X) = V X V^{†}, N (X) = Tr_{B} (V X V^{†}), E (X) = Tr_{R} (V X V^{†}) .$