Hradil, Z.Řeháček, J.Hoz Iglesias, Pablo de laLeuchs, GerdSánchez Soto, Luis Lorenzo2023-06-182023-06-182015-04-271050-294710.1103/PhysRevA.91.042128https://hdl.handle.net/20.500.14352/24033©2015 American Physical Society. We thank G. Toth, H. de Guise, and B.-G. Englert for fruitful discussions. Z.H. and J.R. are thankful for the financial assistance of the Grant Agency of the Czech Republic (Grant No. 15-031945) and the IGA Project of the Palacky University (Grant No. PrF_2015_002). G.L. is partially funded by EU FP7 (Grant No. Q-ESSENCE). Finally, P.H. and L.L.S.-S. acknowledge the support from the Spanish MINECO (Grant No. FIS2011-26786) and UCM-Banco Santander Program (Grant No. GR3/14).Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrodinger-cat-like states, among others.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.91.042128http://journals.aps.org/open access535Phase uncertaintyEigenstate fieldsCoherent statesQuantumGenerationOperatorsLightÓptica (Física)2209.19 Óptica Física