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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Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
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abstract
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.
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representative citing papers
Introduces the Born-Reciprocal Tensor Network to realize UV/IR mixing as an entanglement bridge in renormalization geometry, with a large-volume limit restoring standard Wilsonian decoupling.
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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.
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
A locality-based commutant argument shows that finite-N holographic CFTs lack the protected logical sector required for holographic quantum error correction, leaving only region-by-region entanglement wedge reconstruction.
A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
The paper proposes a kinematic space for any subregion of vacuum AdS, whose geodesic 'PEE threads' uniformly cover the subregion and yield tensor-network models that reproduce Ryu-Takayanagi entropy and realize surface/state and generalized-wedge holography.
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
When the RT area is O(1/G) and bulk entropy O(1), CCKLP-style reconstruction errors are exponentially small in G relative to area-function corrections.
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.
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.
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
The vecro hypothesis introduces a lattice model of the gravitational vacuum whose extended correlations nucleate fuzzballs that destroy semiclassical spacetime near trapped surfaces.
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
Δ^(3)_p is a non-negative signal detecting genuine tripartite entanglement, extended via the E_w = E_p conjecture to holographic systems in AdS3/CFT2.
Generalizes channel-state duality to algebras with centers, establishing a link between state non-separability and channel isometry, plus extension to infinite-dimensional trace-class operators.
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.
The paper claims an FRG derivation of emergent AdS geometry for the O(N) vector model, but the derivation's key step contradicts its own equations.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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.
-
When Renormalisation Remembers: UV/IR Mixing as an Entanglement Bridge
Introduces the Born-Reciprocal Tensor Network to realize UV/IR mixing as an entanglement bridge in renormalization geometry, with a large-volume limit restoring standard Wilsonian decoupling.
-
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.
-
Graph restricted tensors: building blocks for holographic networks
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
-
Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
-
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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Hofstadter's Butterfly in AdS$_3$ Black Holes
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
-
Entanglement Wedge Reconstruction without Holographic Quantum Error Correction
A locality-based commutant argument shows that finite-N holographic CFTs lack the protected logical sector required for holographic quantum error correction, leaving only region-by-region entanglement wedge reconstruction.
-
Phase transitions and uberholography of holographic pure-state geometries
A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
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Holography and Kinematic Space for Gravitational Sub-regions in AdS
The paper proposes a kinematic space for any subregion of vacuum AdS, whose geodesic 'PEE threads' uniformly cover the subregion and yield tensor-network models that reproduce Ryu-Takayanagi entropy and realize surface/state and generalized-wedge holography.
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Subregion observer rules from generalized entanglement wedges
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
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A Note on Corrections to Entanglement Wedge Reconstruction
When the RT area is O(1/G) and bulk entropy O(1), CCKLP-style reconstruction errors are exponentially small in G relative to area-function corrections.
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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.
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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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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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The Entanglement Wedge Polygon
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
-
The magic of the gravitational vacuum
The vecro hypothesis introduces a lattice model of the gravitational vacuum whose extended correlations nucleate fuzzballs that destroy semiclassical spacetime near trapped surfaces.
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ASEP/DSSYK duality and strange correlator
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
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Tripartite Correlation Signal from Multipartite Entanglement of Purification
Δ^(3)_p is a non-negative signal detecting genuine tripartite entanglement, extended via the E_w = E_p conjecture to holographic systems in AdS3/CFT2.
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Channel-State duality with centers
Generalizes channel-state duality to algebras with centers, establishing a link between state non-separability and channel isometry, plus extension to infinite-dimensional trace-class operators.
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The Junction Law for Multipartite Entanglement in Confining Holographic Backgrounds
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.
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Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group via Bulk Metric Reconstruction
The paper claims an FRG derivation of emergent AdS geometry for the O(N) vector model, but the derivation's key step contradicts its own equations.
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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.