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Learning the Alpha-bits of Black Holes
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Learning the Alpha-bits of Black Holes
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When the bulk geometry in AdS/CFT contains a black hole, the boundary reconstruction of a given bulk operator will often necessarily depend on the choice of black hole microstate, an example of state dependence. As a result, whether a given bulk operator can be reconstructed on the boundary at all can depend on whether the black hole is described by a pure state or thermal ensemble. We refine this dichotomy, demonstrating that the same boundary operator can often be used for large subspaces of black hole microstates, corresponding to a constant fraction $\alpha$ of the black hole entropy. In the Schrodinger picture, the boundary subregion encodes the $\alpha$-bits (a concept from quantum information) of a bulk region containing the black hole and bounded by extremal surfaces. These results have important consequences for the structure of AdS/CFT and for quantum information. Firstly, they imply that the bulk reconstruction is necessarily only approximate and allow us to place non-perturbative lower bounds on the error when doing so. Second, they provide a simple and tractable limit in which the entanglement wedge is state-dependent, but in a highly controlled way. Although the state dependence of operators comes from ordinary quantum error correction, there are clear connections to the Papadodimas-Raju proposal for understanding operators behind black hole horizons. In tensor network toy models of AdS/CFT, we see how state dependence arises from the bulk operator being `pushed' through the black hole itself. Finally, we show that black holes provide the first `explicit' examples of capacity-achieving $\alpha$-bit codes. Unintuitively, Hawking radiation always reveals the $\alpha$-bits of a black hole as soon as possible. In an appendix, we apply a result from the quantum information literature to prove that entanglement wedge reconstruction can be made exact to all orders in $1/N$.
Forward citations
Cited by 7 Pith papers
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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.
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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.
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The Page curve of Hawking radiation from semiclassical geometry
Hawking radiation entropy follows the Page curve when quantum extremal surfaces are identified with RT/HRT surfaces in a higher-dimensional holographic dual, making the black hole interior part of the radiation's enta...
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Entanglement Wedge Reconstruction and the Information Paradox
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.
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Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks are introduced as a class satisfying computational covariance, bounding complexity by the Python's Lunch Conjecture exponent, and combining holographic features of perfect and random te...
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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.
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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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