Holograms In Our World

TL;DR

This paper generalizes the concept of entanglement wedges from AdS/CFT to arbitrary spacetimes, defining max- and min-entanglement wedges that capture information flow and entropy properties in quantum gravity.

Contribution

It introduces a new framework for entanglement wedges in general spacetimes, extending holographic ideas beyond AdS/CFT and analyzing their information-theoretic properties.

Findings

Max- and min-entanglement wedges can differ at the classical level.

Information flow is governed by the areas of homology surfaces.

Entanglement wedges obey strong subadditivity and no-cloning principles.

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 $a$.