On the philosophy of cramér-rao-bhattacharya inequalities in quantum statistics to my revered guru c. R. rao for revealing the mystries of chance
Article Type
Research Article
Publication Title
Sankhya: The Indian Journal of Statistics
Abstract
To any parametric family of states of a finite level quantum system we asso-ciate a space of Fisher maps and introduce the natural notions of Cramér-Rao-Bhattacharya tensor and Fisher information form. This leads us to an abstract Cramér-Rao-Bhattacharya lower bound for the covariance matrix of any finite number of unbiased estimators of parameteric functions. A number of illustrative examples are included. Modulo technical assumptions of various kinds our methods can be applied to infinite level quantum systems as well as parametric families of classical probability distributions on Borel spaces.
First Page
521
Last Page
548
Publication Date
1-1-2021
Recommended Citation
Parthasarathy, K. R., "On the philosophy of cramér-rao-bhattacharya inequalities in quantum statistics to my revered guru c. R. rao for revealing the mystries of chance" (2021). Journal Articles. 2183.
https://digitalcommons.isical.ac.in/journal-articles/2183