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Equation 10 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

Symbol D

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}.
DD

What this part means

D occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

D 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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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