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

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.
Comment: 7 pages, 1 figure; v2: corrected the proof of the reconstruction theorem, added new references, acknowledgements, and minor clarifications; v3: added an appendix and minor clarifications, title changed to match PRL version