Improved bounds in entropic uncertainty relations

TL;DR

This paper introduces a new, tighter lower bound for the sum of Shannon entropies in entropic uncertainty relations for pairs of observables in finite-dimensional quantum systems, improving previous bounds.

Contribution

It presents a novel lower bound based on the Landau-Pollak inequality, enhancing the understanding of entropic uncertainty relations for general observables.

Findings

New lower bound improves previous bounds for a wide class of observables.

Relationship between Landau-Pollak inequality and Maassen-Uffink relation analyzed.

Results applicable to finite-dimensional Hilbert spaces.

Abstract

Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel 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 [Maassen and 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.