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In this short note, we examine geodesic distance in Fisher information spacein which the metric is defined by the entanglement entropy in CFT_(1+1). It isobvious in this case that the geodesic distance at a constant time is afunction of the entropy data embedded into the information space. In a specialcase, the geodesic equation can be solved analytically, and we find that thedistance agrees well with the Ryu-Takayanagi formula. Then, we can understandhow the distance looks at the embeded quantum information. The result suggeststhat the Fisher metric is an efficient tool for constructing the holographicspacetime.

Geodesic Distance in Fisher Information Space and Holographic Entropy Formula