  In the estimation theory context, we generalize the notion of Shannon's
entropy power to the R\'{e}nyi-entropy setting. This not only allows to find
new estimation inequalities, such as the R\'{e}nyi-entropy based De Bruijn
identity, isoperimetric inequality or Stam inequality, but it also provides a
convenient technical framework for the derivation of a one-parameter family of
R\'{e}nyi-entropy-power-based quantum-mechanical uncertainty relations. To put
more flesh on the bones, we use the R\'{e}nyi entropy power obtained to show
how the information probability distribution associated with a quantum state
can be reconstructed in a process that is akin to quantum-state tomography. We
illustrate the inner workings of this with the so-called "cat states", which
are of fundamental interest and practical use in schemes such as quantum
metrology. Salient issues, including the extension of the notion of entropy
power to Tsallis entropy and ensuing implications in estimation theory are also
briefly discussed.
