Collision entropy and optimal uncertainty
  We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results in an analytic function of the overlap of the corresponding eigenbases. Besides, we obtain the minimum uncertainty states. We compare our relation with other formulations of the uncertainty principle. 
G. M. Bosyk, M. Portesi and A. Plastino
quant-ph