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.

中文翻译：

---

非退化密度矩阵流形的无参数描述

本文给出了非退化密度矩阵流形中的指数弧的定义，并以此为起点在有限维情况下开发了非参数形式的非交换信息几何。给定Bogoliubov度量，m连接和e连接都是双重的。引入了凸势。它们允许引入双重图表。仿射坐标在末尾引入，以使用更常用的方法建立连接。