  We consider the question of entropic uncertainty relations for prime power
dimensions. In order to improve upon such uncertainty relations for higher
dimensional quantum systems, we derive a tight lower bound amount of entropy
for multiple probability distributions under the constraint that the sum of the
collision probabilities for all distributions is fixed. This is purely a
classical information theoretical result, however using an interesting result
by Larsen \cite{Larsen90} allows us to connect this to an entropic uncertainty
relation.
