Manuscript En05-C@1 · En05-C.tex · proposition · aa213ea6
Proposition: Ordering invariance for specified devices
Stage F: ancestry, matched replacements, and metric bounds › Legal reorderings · lines 1600–1612 · proof included or linked
En05-C@1#prop:ordering
Let a finite dependency partial order compare every pair of devices that are not declared independent. Suppose incomparable devices commute as complete global maps; in particular, disjoint internal Kraus devices satisfy this condition. Every linear extension gives the same complete composite channel.
Proof. Any two linear extensions are connected by adjacent swaps of incomparable events. Each swap leaves the composition unchanged.