Entropic uncertainty relations for successive generalized measurements

Abstract

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.

arXiv comment14 pages and 3 figures

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• Necessary and sufficient condition for joint measurability
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Three-Outcome Qubit Measurements
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Neutron optical test of completeness of quantum root-mean-square errors