@article{bibcite_14958,
  author = {Zbigniew Pucha{\l}a and {\L}. Rudnicki and Karol {\.Z}yczkowski},
  title = {Majorization entropic uncertainty relations},
  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.},
  year = {2013},
  journal = {J. Phys. A: Math. Theor.},
  volume = {46},
  pages = {272002},
  note = {arXiv:1304.7755},
  language = {eng},
}