One-shot holography

• URL: http://arxiv.org/abs/2307.13032v2
• Date: Thu, 11 Apr 2024 18:15:11 GMT
• Title: One-shot holography
• Authors: Chris Akers, Adam Levine, Geoff Penington, Elizabeth Wildenhain,
• Abstract summary: We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture. We extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Following the work of [2008.03319], we define a generally covariant max-entanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on $B$. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.

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