Uncertainty, joint uncertainty, and the quantum uncertainty principle
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/18/3/033019 |
| _version_ | 1797751020114149376 |
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| author | Varun Narasimhachar Alireza Poostindouz Gilad Gour |
| author_facet | Varun Narasimhachar Alireza Poostindouz Gilad Gour |
| author_sort | Varun Narasimhachar |
| collection | DOAJ |
| description | Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations. Our notion relaxes this restriction, revealing previously unexplored joint uncertainty measures. To illustrate the utility of our formalism, we derive an uncertainty relation based on one such new measure. We also use our formalism to gain insight into the conditions under which measure-independent uncertainty relations can be found. |
| first_indexed | 2024-03-12T16:41:17Z |
| format | Article |
| id | doaj.art-3a7d039ce27345bfa95ea8680b39f4b6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:41:17Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-3a7d039ce27345bfa95ea8680b39f4b62023-08-08T14:28:19ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118303301910.1088/1367-2630/18/3/033019Uncertainty, joint uncertainty, and the quantum uncertainty principleVarun Narasimhachar0Alireza Poostindouz1Gilad Gour2Department of Mathematics and Statistics and Institute for Quantum Science and Technology, University of Calgary , 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4Department of Mathematics and Statistics and Institute for Quantum Science and Technology, University of Calgary , 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4Department of Mathematics and Statistics and Institute for Quantum Science and Technology, University of Calgary , 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations. Our notion relaxes this restriction, revealing previously unexplored joint uncertainty measures. To illustrate the utility of our formalism, we derive an uncertainty relation based on one such new measure. We also use our formalism to gain insight into the conditions under which measure-independent uncertainty relations can be found.https://doi.org/10.1088/1367-2630/18/3/033019majorizationjoint uncertaintyuncertainty principle |
| spellingShingle | Varun Narasimhachar Alireza Poostindouz Gilad Gour Uncertainty, joint uncertainty, and the quantum uncertainty principle New Journal of Physics majorization joint uncertainty uncertainty principle |
| title | Uncertainty, joint uncertainty, and the quantum uncertainty principle |
| title_full | Uncertainty, joint uncertainty, and the quantum uncertainty principle |
| title_fullStr | Uncertainty, joint uncertainty, and the quantum uncertainty principle |
| title_full_unstemmed | Uncertainty, joint uncertainty, and the quantum uncertainty principle |
| title_short | Uncertainty, joint uncertainty, and the quantum uncertainty principle |
| title_sort | uncertainty joint uncertainty and the quantum uncertainty principle |
| topic | majorization joint uncertainty uncertainty principle |
| url | https://doi.org/10.1088/1367-2630/18/3/033019 |
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