Holographic Quantum Error Correction and the Projected Black Hole Interior

TL;DR

This paper explores how quantum error correction principles can be used to construct a boundary operator dictionary for black hole interiors in AdS/CFT, demonstrating state-dependent mappings in the SYK model and implications for information transfer.

Contribution

It introduces a method to rewire the holographic dictionary for black hole interiors using projections in the SYK model, highlighting state dependence and information transfer mechanisms.

Findings

Rewiring of the boundary dictionary depends on the projection implemented.

Interior operators can be mapped to the remaining boundary in a determinable way.

Fluidity of the dictionary allows for information transfer between black holes.

Abstract

The quantum error correction interpretation of AdS/CFT establishes a sense of fluidity to the bulk/boundary dictionary. We show how this property can be utilized to construct a dictionary for operators behind horizons of pure black holes. We demonstrate this within the context of the SYK model with pure black hole microstates obtained via projecting out a single side of the thermofield double (and perturbed versions thereof). Assuming an erasure subsystem code for the duality between the eternal black hole and the thermofield double, this projection results in a rewiring of the dictionary so as to map the interior operators to the remaining boundary in a determinable way. We find this dictionary to be sensitive to the implemented projection in a manner reminiscent of previous state-dependent constructions of the black hole interior. We also comment on how the fluidity of the dictionary can be used to transfer information between two black holes connected by a wormhole, relating the ideas of entanglement wedge reconstruction and the Hayden-Preskill decoding criterion.