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Equation 10 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol p_rm e

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}.
pep_{\rm e}

What this part means

prp_rm e is part of the quantity the equation computes from the expression on the right.

Its job in the formula

prp_rm e is part of the quantity the equation computes from the expression on the right.

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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