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

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