Equation 38 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole
Symbol N_perp
What this part means
erp 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
erp is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol N_perp→Article meaning
The passage around this formula
Where this inequality holds, each gate can be treated as evolving under an effectively frozen Hamiltonian for the duration of its own orthogonalization, and the integral above is the natural generalization of the periodic-evolution bound. Where it fails — a gate driven on a timescale comparable to or faster than its own orthogonalization time — the relevant bound is not this integral but the tighter geometric quantum speed limit for explicitly time-dependent driving derived by Deffner and Lutz from the Bures length between the instantaneous states, which reduces to the naive integral only in the slowly-driven limit and otherwise sits below it [ 4 ] . Everything that follows assumes the…
Learn the underlying idea
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Sources cited in the surrounding passage
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