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

Corollary: Robust operational gap

C3: an optimal approximate memory obstruction · lines 883–904 · proof included or linked

En02-C@1#cor:robustgap

At step $3$ , information-theoretic recovery is exact, while any one-slot observer has error at least $1/2$ .

If another consistent emission model has the same access interface and

d_{⋄} (N_{3}, N_{3}) \leq η,

then every one-slot decoder obeys

d_{⋄} (Φ_{π} N_{3}, id_{2}) \geq max {0, 1/2 - η} .

Proof. The first assertion combines Theorems thm:C2 and thm:C3. The second follows by the triangle inequality and CPTP contraction under $Φ_{π}$ .

Displayed formulas in this passage