Geometry from divergence functions and complex structures

Abstract

Motivated by the geometrical structures of quantum mechanics, we introduce an almostcomplex structure J on the product M × M of any parallelizable statistical manifold M . Then, we use J to extract a pre-symplectic form and a metric-like tensor on M × M from a divergence function. These tensors may be pulled back to M , and we compute them in the case of an N-dimensional symplex with respect to the Kullback-Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann-Umegaki relative entropy.If available, please cite the published version