Uncertainty Relation for Smooth Entropies

Marco Tomamichel and Renato Renner
Phys. Rev. Lett. 106, 110506 – Published 16 March 2011

Abstract

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data (e.g., a description of the system’s state before measurement), an extended relation which remains valid in the presence of quantum information has been proposed recently [Berta et al., Nature Phys. 6, 659 (2010)]. Here, we generalize this uncertainty relation to one formulated in terms of smooth entropies. Since these entropies measure operational quantities such as extractable secret key length, our uncertainty relation is of immediate practical use. To illustrate this, we show that it directly implies security of quantum key distribution protocols. Our security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model.

  • Received 1 October 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.110506

© 2011 American Physical Society

Authors & Affiliations

Marco Tomamichel* and Renato Renner

  • Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

  • *marcoto@phys.ethz.ch

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Issue

Vol. 106, Iss. 11 — 18 March 2011

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