One-shot holography

TL;DR

This paper introduces covariant entanglement wedges in holography, proving their properties and conjecturing their role in reconstructing bulk regions from boundary data, extending quantum information frameworks to more general settings.

Contribution

It defines covariant max- and min-entanglement wedges, proves their properties, and extends quantum Shannon theory to finite-dimensional von Neumann algebras with nontrivial centers.

Findings

Proved nesting and inclusion properties of entanglement wedges.

Established one-shot quantum focusing conjecture implications.

Extended quantum Shannon theory to von Neumann algebras with centers.

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.