01093nas a2200145   4500000000100000008004100001100002300042700001900065700002200084700002200106245004600128856004000174490000700214520072600221       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>