Information Geometry and Holographic Correlators

TL;DR

This paper investigates the quantum information geometry of conformal field theories, computing holographic four-point function metrics and their corrections, revealing asymptotic AdS behavior and encoding operator information.

Contribution

It introduces a holographic approach to quantum information geometry, including corrections from bulk Witten diagrams, and relates correlator properties to geometric features.

Findings

The information metric encodes non-identity operators via cross terms.

The metric is asymptotically Anti-de Sitter (AdS).

Transition amplitudes can also be analyzed using this information metric.

Abstract

We explore perturbative corrections to quantum information geometry. In particular, we study a Bures information metric naturally associated with the correlation functions of a conformal field theory. We compute the metric of holographic four-point functions and include corrections generated by tree Witten diagrams in the bulk. In this setting, we translate properties of correlators into the language of information geometry. Cross terms in the information metric encode non-identity operators in the OPE. We find that the information metric is asymptotically AdS. Finally, we discuss an information metric for transition amplitudes.