Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

The pure-state Page–Sen comparison

Coherent entropy, classical records, and the dimension neck › The pure-state Page–Sen comparison · lines 1204–1233

Only when $h = 1$ does the declared fixed pure input become a Haar pure-state ensemble on the vault. Let $m_{0} = min (r, b)$ , $n_{0} = max (r, b)$ , and $H_{j} = \sum_{u = 1}^{j} u^{- 1}$ . Then

E_{U} S (P) = \frac{H _{D} - H _{n_{0}} - ( m _{0} - 1 ) / ( 2 n _{0} )}{ln 2},

E_{U} H (Y) = \frac{H _{D} - H _{b}}{ln 2} .

The first is the established Page–Sen evaluation PageAverage,Sen. The second follows by differentiating the Dirichlet moment

E p_{y}^{s} = \frac{Γ ( b + s ) Γ ( D )}{Γ ( b ) Γ ( D + s )}

and summing over the $r$ outcomes. These pure-ensemble comparisons do not replace Theorem thm:entropy's early-entangled calculation CheungHawk05BC,Hawk06A.

Displayed formulas in this passage

unlabeled · line 1210
$E_{U} S (P) = \frac{H _{D} - H _{n_{0}} - ( m _{0} - 1 ) / ( 2 n _{0} )}{ln 2},$
unlabeled · line 1215
$E_{U} H (Y) = \frac{H _{D} - H _{b}}{ln 2} .$
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$E p_{y}^{s} = \frac{Γ ( b + s ) Γ ( D )}{Γ ( b ) Γ ( D + s )}$