Manuscript Em05-B@1 · Em05-B-v1.tex · definition · 6c050f5b

Definition: Flagged decoder instrument

The specified decoder and its flagged instrument › Visible off-code events · lines 1082–1105

Em05-B@1#def:flagged, Em05-B@1#eq:flagged

Let $K$ be a two-dimensional classical register with labels $c, o$ , meaning code and off-code. Define CP maps

I_{c} (Y) = W^{†} Y W, I_{o} (Y) = Tr ((I_{R} - P) Y) \frac{I _{M^{'}}}{2},

and the complete quantum–classical channel

D_{⋆} (Y) = ∣ c ⟩ ⟨ c ∣_{K} \otimes I_{c} (Y) + ∣ o ⟩ ⟨ o ∣_{K} \otimes I_{o} (Y) .

Displayed formulas in this passage

Em05-B@1#eq:flagged · line 1095
$D_{⋆} (Y) = ∣ c ⟩ ⟨ c ∣_{K} \otimes I_{c} (Y) + ∣ o ⟩ ⟨ o ∣_{K} \otimes I_{o} (Y) .$
unlabeled · line 1087
$I_{c} (Y) = W^{†} Y W, I_{o} (Y) = Tr ((I_{R} - P) Y) \frac{I _{M^{'}}}{2},$