  An entropic approach to formulating uncertainty relations for the
number-annihilation pair is considered. We construct some normal operator that
traces the annihilation operator as well as commuting quadratures with a
complete system of common eigenfunctions. Expanding the measured wave function
with respect to them, one obtains a relevant probability distribution. Another
distribution is naturally generated by measuring the number operator. Due to
the Riesz-Thorin theorem, there exists a nontrivial inequality between
corresponding functionals of the above distributions. We find the bound in this
inequality and further derive uncertainty relations in terms of both the Renyi
and Tsallis entropies. Entropic uncertainty relations for continuous
distribution as well as relations for discretized one are presented.
