Berlin 2014 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 13: Poster (permanent Mo-Do)
MP 13.4: Poster
Tuesday, March 18, 2014, 08:00–18:00, SPA Foyer
Strong majorization entropic uncertainty relations — •Łukasz Rudnicki1,2, Zbigniew Puchała3,4, and Karol Zyczkowski2,4 — 1Freiburg Institute for Advanced Studies, Albert-Ludwigs University of Freiburg, Albertstrasse 19, 79104 Freiburg, Germany — 2Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02-668 Warsaw, Poland — 3Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland — 4Institute of Physics, Jagiellonian University, ul Reymonta 4, 30-059 Kraków, Poland
We present new entropic uncertainty relations in a finite-dimensional Hilbert space. Using the majorization technique we derive several explicit lower bounds for the sum of two Rényi entropies of the same order. Obtained bounds are expressed in terms of the largest singular values of given unitary matrices. Numerical simulations with random unitary matrices show that our bound is almost always stronger than the well known result of Maassen and Uffink.