Entanglement Wedges from Information Metric in Conformal Field Theories

TL;DR

This paper introduces a method to derive entanglement wedge geometries directly from conformal field theories using the Bures information metric, successfully reproducing holographic results for certain CFTs and subsystems.

Contribution

It demonstrates a novel approach linking the Bures metric in CFTs to entanglement wedge geometry in holography, including phase transition features.

Findings

Reproduces entanglement wedges from Bures metric in holographic CFTs

Identifies absence of sharp structures in free scalar CFTs

Accurately captures phase transitions for disconnected intervals

Abstract

We present a new method of deriving the geometry of entanglement wedges in holography directly from conformal field theories (CFTs). We analyze an information metric called the Bures metric of reduced density matrices for locally excited states. This measures distinguishability of states with different points excited. For a subsystem given by an interval, we precisely reproduce the expected entanglement wedge for two dimensional holographic CFTs from the Bures metric, which turns out to be proportional to the AdS metric on a time slice. On the other hand, for free scalar CFTs, we do not find any sharp structures like entanglement wedges. When a subsystem consists of disconnected two intervals we manage to reproduce the expected entanglement wedge from holographic CFTs with correct phase transitions, up to a very small error, from a quantity alternative to the Bures metric.