Manuscript Oai211-A@1 · Oai211-A.tex · section · 3f3e4f63

The complete-complement theorem, locally stated

Metric convergence and quantum recovery are separate › The complete-complement theorem, locally stated · lines 1571–1584

A finite recovery interface is an isometry

V : C ⟶ R \otimes B,

with accessible and complementary channels

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

Every preparation purifier and unreturned quantum output belongs to the complete $B$ .

Displayed formulas in this passage

unlabeled · line 1574
$V : C ⟶ R \otimes B,$
unlabeled · line 1578
$N (X) = Tr_{B} (V X V^{†}), C (X) = Tr_{R} (V X V^{†}) .$