Luis Aina, AlfredoRodil, Alfonso2023-06-192023-06-192013-03-071050-294710.1103/PhysRevA.87.034101https://hdl.handle.net/20.500.14352/34663©2013 American Physical Society. A.L. acknowledges support from Projects No. FIS2012-35583 of the Spanish Ministerio de Economia y Competitividad, and No. QUITEMAD S2009-ESP-1594 of the Comunidad de Madrid.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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.87.034101http://journals.aps.org/open access535Entropic uncertaintyPhase measurementComplementary observablesOptical-phaseInformationStandardStatisticsMechanicsPrincipleGeometryÓptica (Física)2209.19 Óptica Física