English

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

High Energy Physics - Theory 2016-07-14 v3 General Relativity and Quantum Cosmology Quantum Physics

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 AA, 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.

Keywords

Cite

@article{arxiv.1601.05416,
  title  = {Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality},
  author = {Xi Dong and Daniel Harlow and Aron C. Wall},
  journal= {arXiv preprint arXiv:1601.05416},
  year   = {2016}
}

Comments

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