Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertaint...
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MDPI AG
2019-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/21/3/270 |
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| author | Kyunghyun Baek Hyunchul Nha Wonmin Son |
| author_facet | Kyunghyun Baek Hyunchul Nha Wonmin Son |
| author_sort | Kyunghyun Baek |
| collection | DOAJ |
| description | We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Życzkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Życzkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen–Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables. |
| first_indexed | 2024-04-13T07:48:52Z |
| format | Article |
| id | doaj.art-42e92643ec974dd5b1949ecbf0a783ca |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T07:48:52Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-42e92643ec974dd5b1949ecbf0a783ca2022-12-22T02:55:36ZengMDPI AGEntropy1099-43002019-03-0121327010.3390/e21030270e21030270Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized MeasurementsKyunghyun Baek0Hyunchul Nha1Wonmin Son2Department of Physics, Texas A&M University at Qatar, Education City, P.O. Box 23874 Doha, QatarDepartment of Physics, Texas A&M University at Qatar, Education City, P.O. Box 23874 Doha, QatarDepartment of Physics, Sogang University, Mapo-gu, Shinsu-dong, Seoul 121-742, KoreaWe derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Życzkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Życzkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen–Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.http://www.mdpi.com/1099-4300/21/3/270entropic uncertainty relationsdirect-sum majorization relationpositive-operator-valued measure |
| spellingShingle | Kyunghyun Baek Hyunchul Nha Wonmin Son Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements Entropy entropic uncertainty relations direct-sum majorization relation positive-operator-valued measure |
| title | Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements |
| title_full | Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements |
| title_fullStr | Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements |
| title_full_unstemmed | Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements |
| title_short | Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements |
| title_sort | entropic uncertainty relations via direct sum majorization relation for generalized measurements |
| topic | entropic uncertainty relations direct-sum majorization relation positive-operator-valued measure |
| url | http://www.mdpi.com/1099-4300/21/3/270 |
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