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Equation 12 · Part 2 · How Fast Can a Horizon Learn Which Path You Took?

Symbol p

h2(p)=−plog⁡2p−(1−p)log⁡2(1−p)h_2(p)=-p\log_2p-(1-p)\log_2(1-p)
pp

What this part means

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

where h2(p)=−plog⁡2p−(1−p)log⁡2(1−p)h_2(p)=-p\log_2p-(1-p)\log_2(1-p). 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?

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Learn the underlying idea

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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Sources cited in the surrounding passage

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