Tomography from Entanglement

TL;DR

This paper demonstrates how to reconstruct the bulk stress-energy tensor in holography from boundary entanglement data, revealing deep connections between quantum information measures and bulk matter properties.

Contribution

It introduces a method to invert the Ryu-Takayanagi formula for any state to obtain local bulk stress-energy tensor from boundary entanglement.

Findings

Reconstruction of bulk stress-energy tensor from boundary entanglement.

Positivity and convexity of relative entropy imply energy conditions in the bulk.

Information theoretical interpretation of convexity via Fisher metric.

Abstract

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.