Statement
Problem 4.4 of Goto et al.: which specific features of quantum error correction are actually needed to describe quantum gravity? Given non-isometric bulk-to-boundary maps and only-approximate holographic codes, does QG require full QI protection, or only a relaxed version?
Why It Matters
Peripheral to the group’s programs, but conceptually adjacent to the type III₁ / operator-algebra thread: operator-algebra QEC (OAQECC) is the infinite-dimensional generalization that links QEC to the algebras the group works with — so this problem shares mathematical furniture with quantum-information-in-infinite-dimensions.
What We Know
- Holographic codes are approximate and, at finite , non-isometric (Akers–Penington).
- Entanglement-wedge reconstruction is operator-algebra QEC.
- “Full protection” (exact QEC) is likely too strong; the useful notion is approximate/algebraic.
Possible Approaches
- Identify the minimal QEC property that reproduces holographic reconstruction.
- Formulate via OAQECC on von Neumann algebras.