Can Čencov meet Petz?

Abstract

We discuss how to exploit the recent formulation of classical and quantum information geometry in terms of normal states on $W^{\ast }$-algebras to formulate a problem that unifies Cencov's theorem and Petz's theorem.

9 pages - Comments are welcome!

References in corpus (2)

• From the Jordan product to Riemannian geometries on classical and quantum states
• Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras