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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Entanglement Wedge Reconstruction via Universal Recovery Channels
11 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.
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A phase transition in the quantum RT surface at the Page time derives the Page curve and enables entanglement wedge reconstruction of the black hole interior from Hawking radiation.
A proto-area family defines a bulk geometry only when it sews through a single boundary-length map, with a gauge-invariant two-jet criterion and BKM–Jacobi matching as necessary and sufficient conditions.
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
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.
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.
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.
The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.
A modified semiclassical holographic dictionary is used to construct an extended gravitational path integral that factorizes, reproduces the Page curve for entropy, and includes operators for baby universe states.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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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.