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Equation 87 · Part 2 · The Bit Comes Back Before the Bearing

Symbol epsilon

tL(ϵ)t_L(\epsilon)
ϵ\epsilon

What this part means

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

Its job in the formula

epsilon 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

…hand-computable corroboration of the folklore “each extra collected qubit roughly halves what is left to recover,” not a re-derivation of Hayden and Preskill’s original bound, and it is why tL(ϵ)t_L(\epsilon) depends on ϵ\epsilon only logarithmically: driving ϵ\epsilon from 10^{-1} to 10^{-9} costs on the order of thirty extra qubits of radiation, a negligible addition to t∗t_* for any astrophysically sized hole. None of this requires the hole’s dynamics to be literally Haar-random for an unbounded time; Harrow and…

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