Hamilton-Jacobi Theory and Information Geometry

Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function $D$ to be known and we look for a Lagrangian function $\mathfrak{L}$ for which $D$ is a complete solution of the associated Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to replace probability distributions with probability amplitudes.Comment: 8 page

Geometric Measures of Quantum Correlations with Bures and Hellinger Distances

This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.Comment: to be published as a chapter of the book "Lectures on general quantum correlations and their applications" edited by F. Fanchini, D. Soares-Pinto, and G. Adesso (Springer, 2017); 47 pages, 3 figures; second version: minor typos in the first version correcte