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.

arXiv comment9 pages - Comments are welcome!

References in corpus (7)

• Dynamical Vector Fields on the Manifold of Quantum States
• From the Jordan product to Riemannian geometries on classical and quantum states
• Manifolds of classical probability distributions and quantum density operators in infinite dimensions
• Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
• Stratified Manifold of Quantum States, actions of the complex special linear group
• Strict Positivity and $D$-Majorization
• Parametric models and information geometry on W*-algebras