Bulk Locality and Entanglement Swapping in AdS/CFT

TL;DR

This paper demonstrates that simple entanglement swapping models can qualitatively replicate gravitational backreaction and Ryu-Takayanagi predictions in AdS/CFT, highlighting the role of entanglement and code subspace structures.

Contribution

It introduces entanglement swapping operators as models for bulk excitations, capturing key features of gravitational backreaction and code subspace structures in AdS/CFT.

Findings

Models reproduce qualitative features of gravitational backreaction

Entanglement swapping operators align with Ryu-Takayanagi predictions

Boundary Reeh-Schlieder theorem implications for operator equivalence

Abstract

Localized bulk excitations in AdS/CFT are produced by operators which modify the pattern of entanglement in the boundary state. We show that simple models--consisting of entanglement swapping operators acting on a qubit system or a free field theory--capture qualitative features of gravitational backreaction and reproduce predictions of the Ryu-Takayanagi formula. These entanglement swapping operators naturally admit multiple representations associated with different degrees of freedom, thereby reproducing the code subspace structure emphasized by Almheiri, Dong, and Harlow. We also show that the boundary Reeh-Schlieder theorem implies that equivalence of certain operators on a code subspace necessarily breaks down when non-perturbative effects are taken into account (as is expected based on bulk arguments).