01275nas a2200145   4500000000100000008004100001100001700042700002200059700002200081245005500103856004700158300001100205490000700216520090600223       2014                            d1 aŁ. Rudnicki1 aZbigniew Puchała1 aKarol Życzkowski00aStrong Majorization Entropic Uncertainty Relations  uhttps://doi.org/10.1103/PhysRevA.89.052115  a0521150 v893 a<p>We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [ArXiv:1307.4265], which are known to be stronger than the well known result of Maassen and Uffink. Furthermore, we find a novel bound based on majorization techniques, which also happens to be stronger than the recent results involving largest singular values of submatrices of the unitary matrix connecting both bases. The firsts set of new bounds give better results for unitary matrices close to the Fourier matrix, while the second one works better in the opposite sectors. Some results derived admit generalization to arbitrary mixed states and the bounds are increased by the von Neumann entropy of the measured state</p>