Improved bounds on entropic uncertainty relations

5 pages, 1 figure.-- PACS nrs.: 03.65.-w; 03.65.Ta; 03.67.−a.-- ArXiv pre-print available at: http://arxiv.org/abs/0709.1438Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a lower bound on the entropy sum for general pairs of observables in finite-dimensional Hilbert space, which improves on the best bound known to date [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)] for a wide class of observables. This result follows from another formulation of the uncertainty principle, the Landau-Pollak inequality, whose relationship to the Maassen-Uffink entropic uncertainty relation is discussed.We acknowledge support by Dirección General de Investigación (Ministerio de Educación y Ciencia) under grant No. MTM2006-13000-C03-02 and by Universidad Carlos III de Madrid and Comunidad Autónoma de Madrid (project No. CCG06-UC3M/ESP-0690). J. S.-R. was also supported by the DGI (MEC) grant FIS2005-00973 and the Junta de Andalucía research group FQM-0207.Publicad