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Holograms In Our World
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abstract
In AdS/CFT, the entanglement wedge EW$(B)$ is the portion of the bulk geometry that can be reconstructed from a boundary region $B$; in other words, EW$(B)$ is the hologram of $B$. We extend this notion to arbitrary spacetimes. Given any gravitating region $a$, we define a max- and a min-entanglement wedge, $e_{\rm max}(a)$ and $e_{\rm min}(a)$, such that $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$. Unlike their analogues in AdS/CFT, these two spacetime regions can differ already at the classical level, when the generalized entropy is approximated by the area. All information outside $a$ in $e_{\rm max}(a)$ can flow inwards towards $a$, through quantum channels whose capacity is controlled by the areas of intermediate homology surfaces. In contrast, all information outside $e_{\rm min}(a)$ can flow outwards. The generalized entropies of appropriate entanglement wedges obey strong subadditivity, suggesting that they represent the von Neumann entropies of ordinary quantum systems. The entanglement wedges of suitably independent regions satisfy a no-cloning relation. This suggests that it may be possible for an observer in $a$ to summon information from spacelike related points in $e_{\rm max}(a)$, using resources that transcend the semiclassical description of $a$.
Forward citations
Cited by 8 Pith papers
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Fundamental Complement of a Gravitating Region
A gravitating region's hologram is the spacelike complement of the hologram of its fundamental complement, generalizing entanglement-wedge complementarity to arbitrary spacetimes and recovering AdS/CFT.
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Algebras for generalized entanglement wedges
Generalized (Bousso–Penington) entanglement wedges are conjectured to carry von Neumann algebras such that S_gen(W) = S(ω|A_W) − log Ind(E) + K_Ω (eq. 2.7), making BP's monotonicity and strong subadditivity consequenc...
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Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral
The entropy of a bulk region in holographic states equals the generalized entropy of the smallest wedge containing it, derived from a replica path integral via a hollow-graphic construction.
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Combinatorial aspects of holographic quantum secret sharing
Bulk regions in AdS3/CFT2 get a holographic secret-sharing distance d and thresholds (r,s), with r = n - d + 1; pure states satisfy s = d - 1 while mixed states can satisfy s >= d.
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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 surfac...
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Entanglement Entropy of Quantum Corners
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
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The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes
A closed universe in AdS/CFT is not ruled out by recent SWAP-test arguments; the one-dimensional Hilbert space seen from the CFT is external indistinguishability, and CFT data can reconstruct the closed universe's geometry.
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Emergent Holographic Spacetime from Quantum Information
Takayanagi's essay outlines a research program in which holographic spacetime, including the time direction, may emerge from entanglement, complexity, and complex-valued pseudo-entropy, without presenting a new derivation.
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