Must the black hole interior be reconstructed by state-dependent operators?
In plain words
To describe the inside of a black hole using only outside quantities, some proposals let the translation rules depend on which quantum state the black hole is in. Critics argue that this conflicts with the linearity of quantum mechanics.
Precise statement
In AdS/CFT with a single-sided black hole of entropy S, determine whether operators acting on modes behind the horizon can be represented by fixed linear operators on the boundary Hilbert space for all typical states, or whether the representation must depend on the state (Papadodimas-Raju construction). Answer yes (state dependence is necessary) or no, with a proof or an explicit state-independent construction, and state whether non-isometric code models of the interior evade the requirement.
What would settle it
A theorem on the existence of state-independent interior operators for typical black hole states in a holographic theory, or an explicit construction.
Status in the literature
Unverified note
Non-isometric code models (Akers, Engelhardt, Harlow, Penington, Vardhan 2022) give state-independent encodings for states of subexponential complexity; the general question is contested as of 2026.