Optimality of entropic uncertainty relations

2015/09/01 by Kais Abdelkhalek, Abdelkhalek, Kais, René Schwonnek +13
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1509.00398

24 pages, 10 figures

arxiv created 2015/09/01 · arxiv updated 2015/09/02

Abstract

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work we establish optimal uncertainty relations by characterising the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalise various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.

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