Large deviation principle for moment map estimation

Alonso Botero, Matthias Christandl, Péter Vrana

Published 2020-04-29Version 1

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability distributions converge to the value of the moment map. For invertible states we prove that the measures satisfy the large deviation principle with an explicitly given rate function.