Manuscript Hawk07-B@1 · Hawk07-B.tex · section · b9785538

Entropy predictions and a genuinely scaled turnover theorem

Entropy predictions and a genuinely scaled turnover theorem · lines 1094–1106

Fix a pure payload input $∣ ψ ⟩$ independently of $U$ . After tracing $E$ , the vault state is

ρ_{vault}^{U} = h^{- 1} U P_{ψ} U^{†}, rank P_{ψ} = h .

This is generally a mixed random-projector ensemble. The entropy below is that of late radiation $P_{k}$ , not automatically that of the full receiver $P_{k} E$ .

Displayed formulas in this passage

unlabeled · line 1099
$ρ_{vault}^{U} = h^{- 1} U P_{ψ} U^{†}, rank P_{ψ} = h .$

Nearby in this section

lemma: Lemma: Late-radiation purity and rank
section: Entropy predictions and a genuinely scaled turnover theorem
theorem: Theorem: Scaled turnover with recovery and a one-qubit cutoff
corollary: Corollary: Full-diamond version
section: Entropy predictions and a genuinely scaled turnover theorem