Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

The independent complete-channel criterion

Stage 3: modular null cuts and recovery are different interfaces › The independent complete-channel criterion · lines 1235–1248

Let $C ≅ C^{d}$ , $d \geq 2$ , and supply a finite isometry

W : C \to R \otimes B .

Define its accessible channel and complete complement:

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

The complement includes every inaccessible output and any preparation purification.

Displayed formulas in this passage

unlabeled · line 1238
$W : C \to R \otimes B .$
unlabeled · line 1242
$N (X) = Tr_{B} (W X W^{†}), C (X) = Tr_{R} (W X W^{†}) .$