Berlin 2014 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 1: Quanten-Information I
MP 1.2: Talk
Monday, March 17, 2014, 15:20–15:40, SPA SR125
Optimality of entropic uncertainty relations — •Kais Abdelkhalek1, Jörg Duhme1, Berthold-Georg Englert2, Fabian Furrer3, Hans Maassen4, Philippe Raynal2, René Schwonnek1, and Reinhard F. Werner1 — 1Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, Germany — 2Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore — 3Department of Physics, Graduate School of Science, University of Tokyo, Tokyo, Japan — 4Department of Mathematics, Radboud University, Nijmegen, The Netherlands
We investigate the optimality of the entropic uncertainty relation proven by Maassen and Uffink and its generalisation to side information from Berta et al for observables, for which the lower bound attains its maximal value. Here, we call an uncertainty relation optimal if the lower bound can be attained for any value of either of the corresponding uncertainties. We show that the uncertainty relation with side information cannot be optimised. In the case of the Maassen-Uffink uncertainty relation, we disprove a conjecture by Englert et al and provide a characterisation of those states that parametrise the optimal lower bound. This leads to a new conjecture.