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
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.