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

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

Equation 12 · Evolutionary Physics

How Fast Can a Horizon Learn Which Path You Took?

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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