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Entropy 2018, 20(5), 354; https://doi.org/10.3390/e20050354

Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length

Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, 664003 Irkutsk, Russia
Received: 30 March 2018 / Revised: 1 May 2018 / Accepted: 7 May 2018 / Published: 9 May 2018
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
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Abstract

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. Here, specific features of measurements of observables with continuous spectra should be taken into account. First, we formulated uncertainty relations in terms of Shannon entropies. Since such relations involve a state-dependent correction term, they generally differ from preparation uncertainty relations. This difference is revealed when the position is measured by the first. In contrast, state-independent uncertainty relations in terms of Rényi and Tsallis entropies are obtained with the same lower bounds as in the preparation scenario. These bounds are explicitly dependent on the acceptance function of apparatuses in momentum measurements. Entropic uncertainty relations with binning are discussed as well. View Full-Text
Keywords: generalized uncertainty principle; successive measurements; minimal observable length; Rényi entropy; Tsallis entropy generalized uncertainty principle; successive measurements; minimal observable length; Rényi entropy; Tsallis entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rastegin, A.E. Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length. Entropy 2018, 20, 354.

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