Quantum Error Correction and Holographic Information from Bilocal Holography

TL;DR

This paper explores bilocal holography as a method for bulk reconstruction in higher spin theories, demonstrating its natural error correction properties and implications for entanglement and bulk-boundary relations.

Contribution

It introduces a complete bulk/boundary mapping via bilocal holography that does not rely on input from the gravitational dual, highlighting its error correction and entanglement properties.

Findings

Bilocal holography reproduces quantum error correction in holography.

It provides robust bulk (entanglement wedge) reconstruction.

Finite N relations connect boundary and bulk degrees of freedom.

Abstract

Bilocal holography is a constructive approach to the higher spin theory holographically dual to $O(N)$ vector models. In contrast to other approaches to bulk reconstruction, bilocal holography does not take input from the dual gravitational theory. The resulting map is a complete bulk/boundary mapping in that it maps the complete set of $O(N)$ invariant degrees of freedom in the CFT, to the complete set of higher spin degrees of freedom. After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holography and it gives a robust bulk (entanglement wedge) reconstruction. A gauge invariant entangled pair of CFT degrees of freedom are naturally smeared over a semicircle in the bulk spacetime, which is highly suggestive of bit threads. Finally, we argue that finite $N$ relations in the CFT, when interpreted in the dual AdS spacetime, can provide relations between degrees of freedom located near the boundary and degrees of freedom deep in the bulk.