Seminar

Geometry, Mechanics and Control Seminar

Potential functions in information geometry, quantum and classical

Speaker:  Giuseppe Marmo (Università di Napoli "Federico II”, Italy)
Date:  Friday, 08 April 2022 - 15:30
Online:   us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Abstract:

After one century of Quantum Mechanics , there is a widespread belief that "classical descriptions" should be derivable from "quantum descriptions”. In this talk we will show how Fisher-Rao metric ,considered in statistical manifolds,may be derived from Fubini-Study metric on the complex projective space ( pure quantum states) associated with a Hilbert space.
More generally ,on the space of quantum states ( quantum probabilities) quantum metrics will decompose into a "classical part" (defined on a simplex of classical probability distributions) and a "purely quantum part" defined on Kahlerian orbits of state-dependent actions of the unitary group (the "phase-group”). These metric may be obtained from suitable potentials ( “generalized relative entropies" )defined on pair groupoids or general Lie groupoids.