Manuscript Hawk04-C@1 · Hawk04-C-v1.tex · section · 94d46352

Nonconstant residual does not locate the entire code

Row 6: thermality, classical records, and information loss › Nonconstant residual does not locate the entire code · lines 1381–1402

Hawk04-C@1#eq:basis-copy

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For

V_{copy} ∣ i ⟩ = ∣ i ⟩_{R} ∣ i ⟩_{B},

each marginal channel is computational dephasing. Both are nonconstant, and neither recovers the full unknown code by Theorem thm:exact. The relative phases remain available jointly.

By contrast, $V_{hidden}$ has a nonconstant residual channel which does recover the entire code. Thus the assertion

“the complement is nonconstant, so neither factor recovers”

is false. The correct inference is only that $R$ does not exactly recover. Residual-only recovery additionally requires constancy of $N$ .

Displayed formulas in this passage

Hawk04-C@1#eq:basis-copy · line 1384
$V_{copy} ∣ i ⟩ = ∣ i ⟩_{R} ∣ i ⟩_{B},$
unlabeled · line 1396
$“the complement is nonconstant, so neither factor recovers”$