Information metric from Riemannian superspaces

► The meaning of the probability distribution in physical systems described by Riemannian non-degenerated superspaces was explored. ► A new generalization of the Hitchin prescription for constructing the Fisher information metric was presented. ► The metric solution of the non-degenerate superspace establishes a connexion between the Fisher metric and its quantum counterpart. ► We show that this super-quantum mechanical extension of the Fisher metric is described by the CP1 structure of the Fubini-Study metric.