# nLab Fisher metric

Fisher metric is a metric appearing in information geometry, see there for more information and references. There are also several quantum versions. One is the Bures metric and another is quantum Fisher information matrix.

Most references about Fisher metric are at information geometry, here we add few on quantum and $C^*$-algebraic analogues.

• P. Facchi, R. Kulkarni, V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, F. Ventriglia, Classical and quantum Fisher information in the geometrical formulation of quantum mechanics, Physics Letters A 374 pp. 4801 (2010)doi

There is an analogue in free probability

• D.-V. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory. V: Noncommutative Hilbert transforms, Invent. Math. 132:1 (1998) 189–227.

Last revised on November 4, 2019 at 16:07:40. See the history of this page for a list of all contributions to it.