Parameter-free description of the manifold of non-degenerate density matrices

Abstract

The paper gives a definition of exponential arcs in the manifold of non-degenerate density matrices and uses it as a starting point to develop a parameter-free version of non-commutative Information Geometry in the finite-dimensional case. Given the Bogoliubov metric the m- and e-connections are each other dual. Convex potentials are introduced. They allow to introduce dual charts. Affine coordinates are introduced at the end to make the connection with the more usual approach.