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Equation 10 · Part 12 · How Fast Can a Horizon Learn Which Path You Took?

Numerator: 1-sqrt1-V(T)^2

pe(T)=1−D(T)2=1−1−V(T)22.p_{\rm e}(T)=\frac{1-D(T)}{2} =\frac{1-\sqrt{1-V(T)^2}}{2}.
1−1−V(T)21-\sqrt{1-V(T)^2}

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1-sqrt1-V(T)^2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Helstrom’s binary decision theory supplies the minimum average probability of guessing the wrong path: pe(T)=1−D(T)2=1−1−V(T)22p_{\rm e}(T)=\frac{1-D(T)}{2} =\frac{1-\sqrt{1-V(T)^2}}{2}. For the balanced pure-state problem, the minimum-error measurement induces a symmetric binary channel. Its recovered decision information is

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

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