Improved bounds on entropic uncertainty relations

Julio I. de Vicente and Jorge Sánchez-Ruiz
Phys. Rev. A 77, 042110 – Published 16 April 2008

Abstract

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.

  • Figure
  • Received 25 September 2007

DOI:https://doi.org/10.1103/PhysRevA.77.042110

©2008 American Physical Society

Authors & Affiliations

Julio I. de Vicente1 and Jorge Sánchez-Ruiz1,2

  • 1Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
  • 2Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain

Comments & Replies

Comment on “Improved bounds on entropic uncertainty relations”

G. M. Bosyk, M. Portesi, A. Plastino, and S. Zozor
Phys. Rev. A 84, 056101 (2011)

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Vol. 77, Iss. 4 — April 2008

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