@article {iitisid_0617,
title = {Majorization entropic uncertainty relations},
journal = {J. Phys. A: Math. Theor.},
volume = {46},
year = {2013},
note = {arXiv:1304.7755},
pages = {272002},
abstract = {Entropic 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.},
author = {Zbigniew Pucha{\l}a and {\L}. Rudnicki and Karol {\.Z}yczkowski}
}