Manuscript Hawk02-B@2 · Hawk02-B.tex · proof · 95ea744f

Proof

Hamiltonian perturbations and finite-time certification › Implementation comparisons · lines 953–975

Proof. Lemmas lem:duhamel and lem:telescoping bound the complete dynamics by $e_{comp}$ . Partial trace yields the same accessible comparison. Insert collection and decoder replacements; contractivity gives

d_{⋄} (D L N^{(K)}, D^{(K)} N^{(K)}) \leq e_{tot} .

Add Corollary thm:B5.

The residual comparison follows by partial trace of the complete dynamical comparison, followed by comparison with the ideal product replacement state.

A distance between accessible collection channels does not, by itself, compare their chosen isometries in operator norm. That requires a specified complete comparison or an appropriate Stinespring continuity estimate KSW.

Displayed formulas in this passage

unlabeled · line 958
$d_{⋄} (D L N^{(K)}, D^{(K)} N^{(K)}) \leq e_{tot} .$

Nearby in this section

section: Implementation comparisons
assumption: Assumption: Common-space implementation comparisons
section: Implementation comparisons
remark: Remark: Perturbed energy