Information metric from Riemannian superspaces

Abstract

The Fisher information metric is introduced in order to find the meaning of the probability distribution in classical and quantum systems described by Riemannian non-degenerated superspaces. In particular, the physical rôle played by the coefficients a and a⁎ of the fermionic part of an emergent metric solution, obtained previously (Cirilo-Lombardo, 2012 [1]) is explored. We find that the metric solution of the superspace establishes a connexion between the Fisher metric and its quantum counterpart, corroborating early conjectures by Caianiello et al. This quantum mechanical extension of the Fisher metric is described by the CP1 structure of the Fubini–Study metric, with coordinates a and a⁎.