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Physical Review A

Improved lower bounds for uncertaintylike relationships in many-body systems

Yan Alexander Wang, Emily A. Carter

Published Nov 1, 1999• 2 citations
Publisher

Abstract

We show that employing more stringent inequalities in the derivation of uncertaintylike relationships can improve their accuracy. In particular, Eq. (23) due to Romera et al. [Phys. Rev. A 59, 4064 (1999)] can be further improved using the Faris inequalities rather than using the H"older inequalities.
DOI
10.1103/physreva.60.4153

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Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a lower bound on the entropy sum for general pairs of observables in finite-dimensional Hilbert space, which improves on the best bound known to date [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)] for a wide class of observables. This result follows from another formulation of the uncertainty principle, the Landau-Pollak inequality, whose relationship to the Maassen-Uffink entropic uncertainty relation is discussed.