Entropic Uncertainty Relations for Successive Generalized Measurements

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 me...

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Main Authors: Kyunghyun Baek, Wonmin Son
Format: Article
Language:English
Published: MDPI AG 2016-06-01
Series:Mathematics
Subjects:
Online Access:http://www.mdpi.com/2227-7390/4/2/41
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author Kyunghyun Baek
Wonmin Son
author_facet Kyunghyun Baek
Wonmin Son
author_sort Kyunghyun Baek
collection DOAJ
description 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.
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spelling doaj.art-76dc0db620524096b9dc78be2e44b6ed2022-12-21T19:20:28ZengMDPI AGMathematics2227-73902016-06-01424110.3390/math4020041math4020041Entropic Uncertainty Relations for Successive Generalized MeasurementsKyunghyun Baek0Wonmin Son1Department of Physics, Sogang University, Mapo-gu, Shinsu-dong, Seoul 121-742, KoreaDepartment of Physics, Sogang University, Mapo-gu, Shinsu-dong, Seoul 121-742, KoreaWe 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.http://www.mdpi.com/2227-7390/4/2/41entropic uncertainty relationssuccessive measurementsunsharpnessdisturbance
spellingShingle Kyunghyun Baek
Wonmin Son
Entropic Uncertainty Relations for Successive Generalized Measurements
Mathematics
entropic uncertainty relations
successive measurements
unsharpness
disturbance
title Entropic Uncertainty Relations for Successive Generalized Measurements
title_full Entropic Uncertainty Relations for Successive Generalized Measurements
title_fullStr Entropic Uncertainty Relations for Successive Generalized Measurements
title_full_unstemmed Entropic Uncertainty Relations for Successive Generalized Measurements
title_short Entropic Uncertainty Relations for Successive Generalized Measurements
title_sort entropic uncertainty relations for successive generalized measurements
topic entropic uncertainty relations
successive measurements
unsharpness
disturbance
url http://www.mdpi.com/2227-7390/4/2/41
work_keys_str_mv AT kyunghyunbaek entropicuncertaintyrelationsforsuccessivegeneralizedmeasurements
AT wonminson entropicuncertaintyrelationsforsuccessivegeneralizedmeasurements