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

What does this equation mean?

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.

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationssqrt1-V(T)^2, qquad V(T)^2+D(T)^2=1
Result or conditionD(T)
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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DD

Symbol D

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

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TT

Symbol T

T is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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VV

Symbol V

V is one of the signed contributions combined to compute the quantity on the left.

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=

=

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

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√

√

Take a square root.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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How to interpret it

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What the article says around this equation

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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