Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
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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 $A$, 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.
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Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifying horizon vacuum and early radiation purity as the same Dirac observable.
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
Bulk single-particle states of a massive Chern-Simons vector in AdS3 produce entanglement entropy corrections that match the CFT replica-trick result for the corresponding primary and descendants at leading and sub-leading orders, with vanishing edge-mode contribution.
Subregion duality fails in AdS/CFT at leading large N, leading to the proposal of subregion complementarity allowing different CFT operators to describe one bulk subregion.
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
Universal compact entanglement islands are obstructed by an entropy bound violation, implying region-dependent interior reconstruction.
In time-reflection-symmetric holographic states, I3 implies vanishing of multiple four-party entanglement measures and bounds those from multi-entropy, though Q4 is not quantitatively bounded by I3.
Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.
Generalized entanglement wedges rephrase the connected wedge theorem in bulk entropy terms, yielding mutual information bounds and a scattering-to-connected-wedge implication that extends to flat spacetimes.
Quantifies that corrections to entanglement wedge reconstruction are exponentially suppressed (in G) relative to state-dependent corrections to the effective area function, assuming area scales as 1/G and entropy as 1.
Semiclassical entanglement entropy in driven 2D CFT states exhibits dynamical phase imprints; the holographic backreacted minimal area matches the CFT result at O(c^0) and verifies the FLM conjecture.
citing papers explorer
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Replica wormholes and the black hole interior
Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
-
Replica Wormholes and the Entropy of Hawking Radiation
Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
-
Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
-
Smooth horizons from topology change in canonical quantum gravity
Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifying horizon vacuum and early radiation purity as the same Dirac observable.
-
Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
-
Precision tests of bulk entanglement: $AdS_3$ vectors
Bulk single-particle states of a massive Chern-Simons vector in AdS3 produce entanglement entropy corrections that match the CFT replica-trick result for the corresponding primary and descendants at leading and sub-leading orders, with vanishing edge-mode contribution.
-
Subregion Complementarity in AdS/CFT
Subregion duality fails in AdS/CFT at leading large N, leading to the proposal of subregion complementarity allowing different CFT operators to describe one bulk subregion.
-
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
-
Probing bulk geometry via pole skipping: from static to rotating spacetimes
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
-
Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
-
Holographic Tensor Networks as Tessellations of Geometry
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
-
Modular Witten Diagrams and Quantum Extremality
Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.
-
Entanglement inequalities, black holes and the architecture of typical states
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
-
Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
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Entanglement spreading and emergent locality in Brownian SYK chains
In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.
-
A Semiclassical Diagnostic for Spacetime Emergence
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
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Entropy bound and the non-universality of entanglement islands
Universal compact entanglement islands are obstructed by an entropy bound violation, implying region-dependent interior reconstruction.
-
Constraints on four-party entanglement in holography
In time-reflection-symmetric holographic states, I3 implies vanishing of multiple four-party entanglement measures and bounds those from multi-entropy, though Q4 is not quantitatively bounded by I3.
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On bulk reconstruction in Lorentzian AdS and its flat space limit
Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
-
Semiclassical algebraic reconstruction for type III algebras
Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.
-
Generalized Entanglement Wedges and the Connected Wedge Theorem
Generalized entanglement wedges rephrase the connected wedge theorem in bulk entropy terms, yielding mutual information bounds and a scattering-to-connected-wedge implication that extends to flat spacetimes.
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A Note on Corrections to Entanglement Wedge Reconstruction
Quantifies that corrections to entanglement wedge reconstruction are exponentially suppressed (in G) relative to state-dependent corrections to the effective area function, assuming area scales as 1/G and entropy as 1.
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Imprints of dynamical phases in semiclassical entanglement entropy in 2D CFT
Semiclassical entanglement entropy in driven 2D CFT states exhibits dynamical phase imprints; the holographic backreacted minimal area matches the CFT result at O(c^0) and verifies the FLM conjecture.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.