Manuscript Psy02-A@1 · Psy02-A.tex · corollary · d92ce402

Corollary: A recovery certificate implies a witness allowance

Environmental dynamics and the two-budget principle › A separately specified coherence witness · lines 1085–1103 · proof included or linked

Psy02-A@1#cor:recovery

On a declared finite code, suppose a decoder $R_{s}$ satisfies

d_{⋄} (R_{s} Λ_{s}, id) \leq r_{s} .

For code states $ρ, Δ ρ$ ,

D_{s} (ρ; Λ, Δ) \geq d_{tr} (ρ, Δ ρ) - 2 r_{s} .

Proof. Apply Theorem thm:witness to $R_{s} Λ_{s}$ and use contraction under the decoder.

Displayed formulas in this passage