Manuscript Em03-B@2 · Em03-B-v2.tex · lemma · c1a0977d
Lemma: Bounded propagator comparison
B4 extraction: explicit swaps and control certificates › Global bounded perturbations and finite leakage domains · lines 1343–1364 · proof included or linked
Em03-B@2#lem:Duhamel
For bounded self-adjoint generators ,
The induced channels, including references and partial traces, have half-diamond distance at most the same bound, capped at one.
Proof. Variation of constants gives
The unitary factors have norm one. For a purified input, output trace distance is at most the norm of the difference of output vectors; then take the supremum and use contractivity.
Displayed formulas in this passage
unlabeled · line 1346
unlabeled · line 1356