Equation 92 · Part 1 · The Bit Comes Back Before the Bearing

Symbol t_*

t_*

t_*

What this part means

the negligible addition to.

Its job in the formula

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

Full expressionSymbol t_*Article meaning

Where the article explains it

This is an exact, 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 $t_L(\epsilon)$ depends on $\epsilon$ only logarithmically: driving $\epsilon$ from 10^{-1} to 10^{-9} costs on the order of thirty extra qubits of radiation, a negligible addition to $t_*$ for any astrophysically sized hole.

The passage around this formula

…Preskill’s original bound, and it is why $t_L(\epsilon)$ depends on $\epsilon$ only logarithmically: driving $\epsilon$ from 10^{-1} to 10^{-9} costs on the order of thirty extra qubits of radiation, a negligible addition to $t_*$ for any astrophysically sized hole. None of this requires the hole’s dynamics to be literally Haar-random for an unbounded time; Harrow and Low showed that circuits of only polynomial depth already approximate the Haar distribution’s first two moments closely enough for arguments like this one…

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Sources cited in the surrounding passage

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