Bulk Locality and Entanglement Swapping in AdS/CFT

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).

13 pages, 2 figures. v2: added new section to discuss quantum effects, agrees with published version

References in corpus (10)

• Towards a derivation of holographic entanglement entropy
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Constructing local bulk observables in interacting AdS/CFT
• Universality of Gravity from Entanglement
• Proof of a Quantum Bousso Bound
• Bulk Emergence and the RG Flow of Entanglement Entropy
• CFT representation of interacting bulk gauge fields in AdS
• Constructing holographic spacetimes using entanglement renormalization

Cited by in corpus (6)

• Learning the Alpha-bits of Black Holes
• The holographic map as a conditional expectation
• Holographic Codes from Hyperinvariant Tensor Networks
• Holographic Relative Entropy in Infinite-dimensional Hilbert Spaces
• Nonperturbative gravity corrections to bulk reconstruction
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes