Is decoding interior partners from Hawking radiation exponentially hard?
In plain words
An observer who wants to test the firewall argument must first extract one particular quantum from the radiation, a very hard computation. If it takes longer than the black hole lives, the paradox can never be tested.
Precise statement
Given the radiation of a black hole of entropy $S$, is distilling the qubit entangled with a given late Hawking mode (the Harlow-Hayden task) quantum-computationally hard, requiring time $\exp(\Omega(S))$ for every quantum algorithm, for realistic black hole dynamics instead of idealized random unitaries? An answer is a reduction to a standard hardness assumption, an unconditional bound, or an efficient algorithm.
What would settle it
A complexity-theoretic proof of hardness for decoding under a physically motivated model of black hole dynamics, or an efficient decoder.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Hardness holds under complexity assumptions (Harlow and Hayden 2013) and was later tied to the existence of quantum cryptographic primitives (2023); realistic dynamics remain open as of 2026.
Parent problems
- Special case of Does an infalling observer see vacuum at an old black hole's horizon? · open · from revision 1
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