Equation 12 · How Fast Can a Horizon Learn Which Path You Took?
What does this equation mean?
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.
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.
Read it piece by piece
Symbol h_2
is part of the quantity the equation computes from the expression on the right.
Symbol p
p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
where . is binary entropy. The first equation inherits quantum minimum-error detection [ 14 ] . The second is ordinary mutual information for the resulting binary channel. It answers a concrete question: if one path bit was chosen fairly and one optimized single-shot yes/no measurement was made, how many bits did that decision convey on average?
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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