Existence of unbiased resilient estimators in discrete quantum systems

Understand

The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation.

• Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator.
• In contrast, Bhattacharyya bounds offer a more robust estimation framework with respect to prior accuracy by introducing additional constraints on the estimator.
• In this work, we examine divergences that arise in the computation of these bounds and establish the conditions under which they remain valid.