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Equation 9 · Part 4 · How Fast Can a Horizon Learn Which Path You Took?

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D(T)=1−V(T)2,V(T)2+D(T)2=1.D(T)=\sqrt{1-V(T)^2}, \qquad V(T)^2+D(T)^2=1.
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

For two pure states, D(T)=1−V(T)2,V(T)2+D(T)2=1D(T)=\sqrt{1-V(T)^2}, \qquad V(T)^2+D(T)^2=1. This is the first translation. A visibility of 0.6 corresponds to a trace distinguishability of 0.8; neither number is a bit count.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.