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Entropic Uncertainty Relations for Successive Generalized Measurements

by Kyunghyun Baek 1 and Wonmin Son 1,2,*
Department of Physics, Sogang University, Mapo-gu, Shinsu-dong, Seoul 121-742, Korea
Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
Author to whom correspondence should be addressed.
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Mathematics 2016, 4(2), 41;
Received: 2 April 2016 / Revised: 24 May 2016 / Accepted: 1 June 2016 / Published: 7 June 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two distinctive operational scenarios. In the first scenario, by merging two successive measurements into one we consider successive measurement scheme as a method to perform an overall composite measurement. In the second scenario, on the other hand, we consider it as a method to measure a pair of jointly measurable observables by marginalizing over the distribution obtained in this scheme. In the course of this work, we identify that limits on one’s ability to measure with low uncertainty via this scheme come from intrinsic unsharpness of observables obtained in each scenario. In particular, for the Lüders instrument, disturbance caused by the first measurement to the second one gives rise to the unsharpness at least as much as incompatibility of the observables composing successive measurement. View Full-Text
Keywords: entropic uncertainty relations; successive measurements; unsharpness; disturbance entropic uncertainty relations; successive measurements; unsharpness; disturbance
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Baek, K.; Son, W. Entropic Uncertainty Relations for Successive Generalized Measurements. Mathematics 2016, 4, 41.

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