Manuscript En02-C@1 · En02-C-v1.tex · theorem · 7549c6df

Theorem: C6: compatible complete-channel error budgets

C6: implementation, model error, and radiation loss · lines 1493–1526 · proof included or linked

En02-C@1#thm:C6

Suppose

d_{⋄} (DN, id_{M}) \leq ϵ_{rec}, d_{⋄} (D, D) \leq ϵ_{impl}, d_{⋄} (N, N) \leq ϵ_{model} .

Then

d_{⋄} (D N, id_{M}) \leq ϵ_{rec} + ϵ_{impl} + ϵ_{model} .

For compatible complete-channel steps with individual errors $δ_{j}$ , the implementation error is at most $\sum_{j} δ_{j}$ .

Proof. Insert $D N$ and $DN$ , use the triangle inequality, and contract under CPTP composition. The stepwise statement follows by telescoping the channel products.

Displayed formulas in this passage

unlabeled · line 1496
$d_{⋄} (DN, id_{M}) \leq ϵ_{rec}, d_{⋄} (D, D) \leq ϵ_{impl}, d_{⋄} (N, N) \leq ϵ_{model} .$
unlabeled · line 1507
$d_{⋄} (D N, id_{M}) \leq ϵ_{rec} + ϵ_{impl} + ϵ_{model} .$

Nearby in this section

section: C6: implementation, model error, and radiation loss