Manuscript Oai276-A@1 · Oai276-A.tex · section · 215068af

Freeze a genuinely thermal, nonunital channel

Stages 3 and 6: the explicit finite maximum certificate › Freeze a genuinely thermal, nonunital channel · lines 838–864

Oai276-A@1#eq:frozen, Oai276-A@1#eq:f, Oai276-A@1#eq:xq

From now on,

γ = \frac{1}{2}, ν = \frac{1}{4}, A = A_{1/2, 1/4} .

The objective in nats is

f (p) := (ln 2) F_{1/2, 1/4} (p) = h_{e} (\frac{p}{2} + \frac{1}{8}) - g_{e} (\frac{3}{32} + \frac{( p - 1/4 ) ^{2}}{4}) .

Define

d (p) = p - \frac{1}{4}, x (p) = \frac{3}{4} - p, q (p) = \frac{5}{8} - d (p)^{2} .

The determinant eigenvalue radius is $q (p)$ .

Displayed formulas in this passage

Oai276-A@1#eq:frozen · line 841
$γ = \frac{1}{2}, ν = \frac{1}{4}, A = A_{1/2, 1/4} .$
Oai276-A@1#eq:f · line 848
$f (p) := (ln 2) F_{1/2, 1/4} (p) = h_{e} (\frac{p}{2} + \frac{1}{8}) - g_{e} (\frac{3}{32} + \frac{( p - 1/4 ) ^{2}}{4}) .$
Oai276-A@1#eq:xq · line 857
$d (p) = p - \frac{1}{4}, x (p) = \frac{3}{4} - p, q (p) = \frac{5}{8} - d (p)^{2} .$