Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Correction

Abstract

Recently, Almheiri, Dong, and Harlow have argued that the localization of bulk information in a boundary dual should be understood in terms of quantum error correction. We show that this structure appears naturally when the gauge invariance of the boundary theory is incorporated. This provides a new understanding of the non-uniqueness of the bulk fields (precursors). It suggests a close connection between gauge invariance and the emergence of spacetime.

5 2-column pages. 2 figures. v2: Added discussion and clarifications. v3: References added, notational improvements, typo corrections, small clarifications

References in corpus (5)

• Holographic representation of local bulk operators
• Constructing local bulk observables in interacting AdS/CFT
• AdS_4/CFT_3 Construction from Collective Fields
• Scanning Tunneling Macroscopy, Black Holes, and AdS/CFT Bulk Locality
• Higher Spin Holography, RG, and the Light Cone

Cited by in corpus (49)

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• Entanglement, Holography and Causal Diamonds
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• Entanglement phase transitions in random stabilizer tensor networks
• Exploring the Tensor Networks/AdS Correspondence
• A toy model of black hole complementarity
• Entwinement in discretely gauged theories
• Contrasting SYK-like Models
• Tensor network and ($p$-adic) AdS/CFT
• TASI Lectures on the Emergence of the Bulk in AdS/CFT
• Majorana dimers and holographic quantum error-correcting codes
• Towards holography via quantum source-channel codes
• Approximate Bacon-Shor Code and Holography
• Locality, bulk equations of motion and the conformal bootstrap
• Precursors, Gauge Invariance, and Quantum Error Correction in AdS/CFT
• Bulk from Bi-locals in Thermo Field CFT
• Code subspaces for LLM geometries
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Explicit reconstruction of the entanglement wedge
• Holography as a highly efficient RG flow I: Rephrasing gravity
• Into the Bulk: A Covariant Approach
• Bulk Locality and Entanglement Swapping in AdS/CFT
• Does boundary quantum mechanics imply quantum mechanics in the bulk?
• Quantum error correction and large $N$
• Quantum error correction and entanglement spectrum in tensor networks
• Holographic relations for OPE blocks in excited states
• Understanding holographic error correction via unique algebras and atomic examples
• Universal Terms of Entanglement Entropy for 6d CFTs
• Explicit reconstruction of the entanglement wedge via the Petz map
• Tensor chain and constraints in tensor networks
• The algebra of observables in Gaußian normal spacetime coordinates
• Precursor problem and holographic mutual information
• Asymmetric interiors for small black holes
• Causal Density Matrices
• Classical Holographic Codes
• A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory
• Cutoff Function in Holographic RG Flow
• Shrinking of Operators in Quantum Error Correction and AdS/CFT
• Flat-space Quantum Gravity in AdS/CFT
• Approximate recovery with locality and symmetry constraints
• Precursors and BRST Symmetry
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• A note on bulk locality and covariance in AdS/CFT
• Holographic Space-time and Quantum Information
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• Quantum Information Approaches to Quantum Gravity
• Kinematics of Horizon and Singularity and IR/UV Mixing in AdS