01106nas a2200157   4500000000100000000000100001008004100002100002300043700001900066700002200085700002200107245004600129856004000175490000700215520072600222       2016                            d1 aRadosław Adamczak1 aRafał Latała1 aZbigniew Puchała1 aKarol Życzkowski00aAsymptotic entropic uncertainty relations  uhttp://dx.doi.org/10.1063/1.49444250 v573 a<p>Entropic uncertainty relations are analyzed for the case of N-dimensional Hilbert space and two orthogonal measurements performed in two generic bases, related by a Haar random unitary matrix U. We derive estimations for the average norms of truncations of U of a given size, which allow us to study state-independent lower bounds for the sum of two entropies describing the measurements outcomes. In particular, we show that the Maassen–Uffink bound asymptotically behaves as lnN−lnlnN−ln2, while the strong entropic majorization relation yields a nearly optimal bound, lnN−const. Analogous results are also obtained for a more general case of several orthogonal measurements performed in generic bases.</p>