Optimal estimation of quantum observables
  We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased estimation is achieved by the usual procedure that consists in performing independent measurements of the observable on each system and averaging the measurement outcomes. 
Giacomo Mauro D'Ariano, Vittorio Giovannetti, and Paolo Perinotti