  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 uncertatinty 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
Schr\"odinger catlike states, among others.
