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Rotated quadratures carry the phase-dependent information of theelectromagnetic field, so they are somehow conjugate to the photon number. Weanalyze this noncanonical pair, finding an exact uncertatinty relation, as wellas a couple of weaker inequalities obtained by relaxing some restrictions ofthe problem. We also find the intelligent states saturating that relation andcomplete their characterization by considering extra constraints on thesecond-order moments of the variables involved. Using these moments, weconstruct performance measures tailored to diagnose photon-added andSchr\"odinger catlike states, among others.

Extremal states for photon number and quadratures as gauges for nonclassicality