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Equation 38 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol A

A(tc)\mathcal A(t_c)
AA

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A is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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A is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Define A(tc)\mathcal A(t_c) as a preregistered set of physically admissible future protocols after the cutoff. It must specify which controls Alice retains, their duration, energy, acceleration, localization, and boundary conditions. For each u∈\inA(tc)\mathcal A(t_c) , let ρ0,Hu\rho^{u}_{0,H} and ρ1,Hu\rho^{u}_{1,H} be the completed conditional states on the declared horizon algebra. Then define an irreducible distinguishability envelope

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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