Luis Aina, Alfredo2023-06-202023-06-202003-03-191050-294710.1103/PhysRevA.67.032108https://hdl.handle.net/20.500.14352/51522©2003 The American Physical SocietyWe generalize to systems with arbitrary finite dimension a measure of quantum fluctuations (the certainty) previously introduced for two-dimensional systems. Using this measure, we study the duality relations satisfied by complementary observables looking for states with minimum joint fluctuations (maximum certainty states). We extend the duality relations to encompass several complementary observables simultaneously.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.67.032108http://journals.aps.org/open access535Entropic uncertainty relationsQuantized radiation-fieldQuantum-phase measurementCertainty relationsInvariant informationOptical-phaseObservablesStatesLocalizationOperatorsÓptica (Física)2209.19 Óptica Física