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Equation 10 · Part 7 · How Fast Can a Horizon Learn Which Path You Took?

√

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}.
√

What this part means

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Its job in the formula

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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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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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