Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

TL;DR

This paper proves a theorem showing that in AdS/CFT, bulk operators within the entanglement wedge can be reconstructed as CFT operators in a boundary subregion, advancing the understanding of holographic duality and quantum error correction.

Contribution

It introduces a simple theorem that extends bulk operator reconstruction to the entanglement wedge, surpassing previous causal wedge limitations.

Findings

Bulk operators in the entanglement wedge can be reconstructed from boundary subregion operators.

The proof combines quantum information theory and quantum error correction concepts.

This work improves the understanding of holographic duality and operator reconstruction.

Abstract

In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the Anti-de Sitter / Conformal Field Theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion $A$, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.