  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.
