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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MDPI AG
2016-06-01
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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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issn | 2227-7390 |
language | English |
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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 |