Entanglement Wedges from the Information Metric in Conformal Field Theories

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 the 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 anti–de Sitter 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 two disconnected intervals, we manage to reproduce the expected entanglement wedge from holographic CFTs with the correct phase transitions, up to a very small error, from a quantity alternative to the Bures metric.