Alternative measures of uncertainty in quantum metrology: Contradictions and limits

We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of minute changes of physical quantities. We show that different measures lead to contradictory conclusions, including the possibility of arbitrarily small uncertainty for fixed resources. These intrinsic performances are compared with the averaged error in the corresponding estimation problem after single-shot measurements.