Statement
Problem 3.3 of Goto et al.: once a reference structure (frame, observer algebra, reference state, code subspace) is fixed, what are the fundamental limits — information-theoretic and computational — on what an observer can extract about the bulk geometry from the microscopic state?
Why It Matters
Peripheral to the group, but it is the complexity-theoretic counterpart of the group’s capacity questions: both ask what is operationally accessible given a bounded agent. Harlow–Hayden / Python’s-Lunch hardness is the black-hole-interior version.
What We Know
- Harlow–Hayden: decoding the interior mode of an old black hole is exponentially complex.
- Python’s Lunch: a geometric obstruction (non-minimal QES) signals exponential reconstruction complexity.
- State-dependent (Papadodimas–Raju) reconstruction has its own accessibility limits.
Possible Approaches
- Separate information-theoretic accessibility (is it there?) from computational accessibility (can a bounded observer get it?).
- Relate complexity obstructions to bulk geometric features (QES structure).