01158nas a2200145   4500000000100000000000100001008004100002100002200043700001700065700002200082245004800104300001100152490000700163520084200170       2013                            d1 aZbigniew Puchała1 aŁ. Rudnicki1 aKarol Życzkowski00aMajorization entropic uncertainty relations  a2720020 v463 aEntropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of Renyi entropies describing probability distributions associated with a given pure state expanded in eigenbases of two observables. The bounds obtained are expressed in terms of the largest singular values of submatrices of the unitary rotation matrix. For a generic unitary matrix of size N = 5 the bound obtained is stronger than the one of Maassen and Uffink (MU) with probability larger than 98%, and this ratio increases with N. We show also that the bounds investigated are invariant for unitary matrices equivalent up to dephasing and permutation and derive a classical analogue of the MU uncertainty relation formulated for stochastic transition matrices.