Information geometry and its applications

Pescara - 1-5 July 2002


Abstract

July 5 - 11.40-12.30
P. Gibilisco, T. Isola - Some open problems in noncommutative Information Geometry

We discuss some of the open problems of the theory of noncommutative alpha-connections and of non-commutative monotone metrics. As an example we show how it is possible to calculate the geodesic distance associated to Wigner-Yanase information from an approach that mimic the classical pull-back approach to Fisher information (note that there exists only another explicit formula of this kind, namely the formula of geodesic distance for the Bures metric).

References
[1] P. Gibilisco, T.Isola, Monotone metrics on statistical manifolds of density matrices by geometry of noncommutative L^2-spaces, in Disordered and Complex Systems, eds. A.C.Coolen, L.Hughston, P.Sollich, R.F.Streater (AIP, 2001), 129-140.

[2] P.Gibilisco, T.Isola. A Characterisation of Wigner-Yanase skew information among statistically monotone metrics. Vol. 4, No. 4 (2001), 553-557. Infinite Dimensional Analysis, Quantum Probability & Related Fields. [an error occurred while processing this directive]