Matia-Hernando, PalomaLuis Aina, Alfredo2023-06-202023-06-202012-11-091050-294710.1103/PhysRevA.86.052106https://hdl.handle.net/20.500.14352/44571©2012 American Physical Society. A.L. acknowledges support from Project No. FIS2008-01267 of the Spanish Direccion General de Investigacion del Ministerio de Ciencia e Innovacion, and from Project No. QUITEMAD S2009-ESP-1594 of the Consejeria de Educacion de la Comunidad de Madrid.We show that variance and Shannon entropy provide contradictory conclusions for the uncertainty associated with the number operator for some families of states of harmonic oscillator systems with fixed mean number, and for the uncertainty of a spin component for states with and without fixed mean. We analyze this behavior in terms of the properties of these uncertainty measures. We explore their impact on quantum metrology, examining the limits to resolution caused by number fluctuations in diverse scenarios of phase-shift detection.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.86.052106http://journals.aps.org/open access535Entropic uncertaintyNonclassical statesPhase measurementHeisenberg limitCoherent statesWigner functionOptical-phaseComplementary observablesInformation principleÓptica (Física)2209.19 Óptica Física