Q-Math Seminar

Can Cencov meet Petz?

Speaker:  Florio M. Ciaglia (UC3M)
Date:  Friday, 27 January 2023 - 13:00
Place:  Room 2.2.D08, Universidad Carlos III de Madrid


Cencov's theorem on the uniqueness of the Fisher-Rao metric tensor and Petz's classification of monotone metric tensors are considered the cornerstones of classical and quantum information geometry, respectively. I will review and discuss these beautiful results with particular attention to a categorical formalization of Petz's classification in analogy with Cencov's ideology, and I will then argue about a possible unification in the framework of Jordan algebras.