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

Corollary: Full-diamond version

Entropy predictions and a genuinely scaled turnover theorem · lines 1229–1241

Hawk07-B@1#cor:scaledturnover

For $d = 4^{s}$ , $s \geq 2$ , and $0 < ε < 1$ , it suffices to choose

ζ = ε^{2} /8, h = 2^{m} \geq \frac{16 d ^{2}}{ε ^{2}} .

Then the family in Theorem thm:turnover has full-diamond error at most $ε$ on all retained cuts. For $d = 16$ , its measure allowance is $1/64$ . For larger $d$ , the proved allowance is $1/ (4 d)$ , not a dimension-independent $1/64$ .

Displayed formulas in this passage

unlabeled · line 1232
$ζ = ε^{2} /8, h = 2^{m} \geq \frac{16 d ^{2}}{ε ^{2}} .$

Nearby in this section

section: Entropy predictions and a genuinely scaled turnover theorem
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
section: Entropy predictions and a genuinely scaled turnover theorem