Embedding Quantum Information into Classical Spacetime: Information Geometrical Perspectives on anti-de Sitter space / conformal field theory Correspondence

TL;DR

This paper explores the AdS3/CFT2 correspondence through an information-geometrical lens, using the Fisher metric to connect classical spacetime geometry with quantum information properties, and finds consistency with known holographic results.

Contribution

It introduces an information-geometrical framework for AdS/CFT, highlighting the Fisher metric's role in relating spacetime geometry to quantum information measures.

Findings

Fisher metric effectively captures the spacetime geometry in AdS3/CFT2.

Quantum state spectra exhibit power-law correlation lengths consistent with conformal dimensions.

Entanglement entropy aligns with the Ryu-Takayanagi formula in this framework.

Abstract

An information-geometrical interpretation of AdS3/CFT2 correspondence is given. In particular, we consider an inverse problem in which the classical spacetime metric is given in advance and then we find what is the proper quantum information that is well stored into the spacetime. We see that the Fisher metric plays a central role on this problem. Actually, if we start with the two-dimensional hyperbolic space, a constant-time surface in AdS3, the resulting singular value spectrum of the quantum state shows power law for the correlation length with conformal dimension proportional to the curvature radius in the gravity side. Furthermore, the entanglement entropy data embedded into the hyperbolic space agree well with the Ryu-Takayanagi formula. These results show that the relevance of the AdS/CFT correspondence can be represented by the information-gemetrical approach based on the Fisher metric.