Geometric approach to extend Landau-Pollak uncertainty relations for   positive operator-valued measures
  We provide a twofold extension of Landau--Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau--Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family. 
G.M. Bosyk, S. Zozor, M. Portesi, T.M. Os\'an, and P.W. Lamberti
quant-ph