Manuscript En01-A@1 · En01-A.tex · example · 558b972b

Example: Exact FR exponents

Statistical detection through a fixed interface · lines 2943–2966

En01-A@1#ex:fr-exponents

At the symmetric point, dephasing record $1$ gives two orthogonal pure sectors of weights $1/3$ and $2/3$ . The coherent state is pure. Therefore

s min tr (ρ^{s} (Δ_{{1}} ρ)^{1 - s}) = (1/3)^{2} + (2/3)^{2} = 5/9,

and

ξ_{C} = lo g (9/5) \approx 0.587787,

D (ρ ∥ Δ_{{1}} ρ) = - \frac{1}{3} lo g \frac{1}{3} - \frac{2}{3} lo g \frac{2}{3} \approx 0.636514.

The Chernoff minimum occurs at the $s = 0$ support-projection endpoint.

Displayed formulas in this passage

unlabeled · line 2948
$s min tr (ρ^{s} (Δ_{{1}} ρ)^{1 - s}) = (1/3)^{2} + (2/3)^{2} = 5/9,$
unlabeled · line 2956
$ξ_{C} = lo g (9/5) \approx 0.587787,$
unlabeled · line 2959
$D (ρ ∥ Δ_{{1}} ρ) = - \frac{1}{3} lo g \frac{1}{3} - \frac{2}{3} lo g \frac{2}{3} \approx 0.636514.$