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

Definition: Decoder and terminal observation

The fixed finite interface · lines 237–255

En07-B@1#def:decoder

A quantum-return decoder is a deterministic CPTP map

D : B (R) ⟶ B (C_{out}),

where $C_{out}$ has a fixed identification with $C$ . Its error is

ε (D; N) = d_{⋄} (D \circ N, id_{C}), ε_{rec} (N) = D in f ε (D; N) .

A subsequent observation of $C_{out}$ is a measurement channel $M \circ D \circ N$ , not the channel $D \circ N$ itself.

Displayed formulas in this passage

unlabeled · line 240
$D : B (R) ⟶ B (C_{out}),$
unlabeled · line 245
$ε (D; N) = d_{⋄} (D \circ N, id_{C}), ε_{rec} (N) = D in f ε (D; N) .$