On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics

Details On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics

2009-07-13

arxiv.org/abs/0907.2210v1

Mathematics

Probability

Scientific paper

To any parametric family of states of a finite level quantum system we associate a space of Fisher maps and introduce the natural notions of Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to an abstract Cram\'er-Rao-Bhattacharya lower bound for the covariance matrix of any finite number of unbiased estimators of parameteric functions. A number of illustrative examples is 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.

Affiliated with

Also associated with

No associations

Rating

On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101250