Manuscript VII-G@1 · VII-G.tex · example · 54f561e8

Example: Deleting a branch is not a channel repair

Balance laws and admissibility without postselection › Complete fallback design · lines 1431–1443

VII-G@1#ex:postselection

If the only retained branch is $Φ (X) = P_{0} X P_{0}$ , its trace is $Tr (P_{0} X)$ , not $Tr X$ . The normalized successful output

ρ ⟼ \frac{P _{0} ρ P _{0}}{Tr ( P _{0} ρ )}

is not a trace-preserving linear map on the full input domain. A complete model must retain an admissible failure branch or another complete fallback.

Displayed formulas in this passage

unlabeled · line 1436
$ρ ⟼ \frac{P _{0} ρ P _{0}}{Tr ( P _{0} ρ )}$

Nearby in this section

proposition: Proposition: Admissible rerouting
section: Complete fallback design