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Equation 12 · Part 5 · How Fast Can a Horizon Learn Which Path You Took?

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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