Causal Holographic Information

TL;DR

This paper introduces a new measure called causal holographic information, based on the area of a specific bulk surface, to quantify the information content of boundary regions in holography, contrasting it with entanglement entropy.

Contribution

It proposes a novel geometric measure of information in holography, linking bulk surface areas to boundary region information content, distinct from entanglement entropy.

Findings

Causal holographic information is defined via a specific extremal surface.

It correlates with entanglement entropy in known microscopic cases.

The measure provides a new perspective on boundary-to-bulk information reconstruction.

Abstract

We propose a measure of holographic information based on a causal wedge construction. The motivation behind this comes from an attempt to understand how boundary field theories can holographically reconstruct spacetime. We argue that given the knowledge of the reduced density matrix in a spatial region of the boundary, one should be able to reconstruct at least the corresponding bulk causal wedge. In attempt to quantify the `amount of information' contained in a given spatial region in field theory, we consider a particular bulk surface (specifically a co-dimension two surface in the bulk spacetime which is an extremal surface on the boundary of the bulk causal wedge), and propose that the area of this surface, measured in Planck units, naturally quantifies the information content. We therefore call this area the causal holographic information. We also contrast our ideas with earlier studies of holographic entanglement entropy. In particular, we establish that the causal holographic information, whilst not being a von Neumann entropy, curiously enough agrees with the entanglement entropy in all cases where one has a microscopic understanding of entanglement entropy.