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Equation 36 · How Fast Can a Horizon Learn Which Path You Took?

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TT

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TT

Symbol T

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The exponential calculation assumes that T labels a completed preparation–hold–recombination protocol. It does not answer how much information has become irrevocable at an intermediate cutoff tct_c . That distinction became unavoidable when Danielson, Kudler-Flam, Satishchandran, and Wald solved a finite-time optimization problem: given the entangling radiation already past a horizon cross-section, what future field purification best preserves Alice’s coherence? Their optimal future can be nonintuitive. Even after Alice has brought the branches together, reopening and manipulating the superposition can sometimes reduce the final decoherence [ 7 ] .

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