Entropic uncertainty relations for multiple measurements assigned with biased weights
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In this paper we investigate Rényi entropic uncertainty rela...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013127 |
| _version_ | 1797210212142153728 |
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| author | Shan Huang Hua-Lei Yin Zeng-Bing Chen Shengjun Wu |
| author_facet | Shan Huang Hua-Lei Yin Zeng-Bing Chen Shengjun Wu |
| author_sort | Shan Huang |
| collection | DOAJ |
| description | The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In this paper we investigate Rényi entropic uncertainty relations (EURs) in the scenario where measurements on individual copies of a quantum system are selected with nonuniform probabilities. In contrast with EURs that characterize an observer's overall lack of information about outcomes with respect to a collection of measurements, we establish state-dependent lower bounds on the weighted sum of entropies over multiple measurements. Conventional EURs thus correspond to the special cases when all weights are equal, and in such cases we show our results are generally stronger than previous ones. Moreover, taking the entropic steering criterion as an example, we numerically verify that our EURs could be advantageous in practical quantum tasks by optimizing the weights assigned to different measurements. Importantly, this optimization does not require quantum resources and is efficiently computable on classical computers. |
| first_indexed | 2024-04-24T10:07:00Z |
| format | Article |
| id | doaj.art-1f703b87853042f5aad608a0765cf4e1 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:00Z |
| publishDate | 2024-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1f703b87853042f5aad608a0765cf4e12024-04-12T17:38:49ZengAmerican Physical SocietyPhysical Review Research2643-15642024-01-016101312710.1103/PhysRevResearch.6.013127Entropic uncertainty relations for multiple measurements assigned with biased weightsShan HuangHua-Lei YinZeng-Bing ChenShengjun WuThe entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In this paper we investigate Rényi entropic uncertainty relations (EURs) in the scenario where measurements on individual copies of a quantum system are selected with nonuniform probabilities. In contrast with EURs that characterize an observer's overall lack of information about outcomes with respect to a collection of measurements, we establish state-dependent lower bounds on the weighted sum of entropies over multiple measurements. Conventional EURs thus correspond to the special cases when all weights are equal, and in such cases we show our results are generally stronger than previous ones. Moreover, taking the entropic steering criterion as an example, we numerically verify that our EURs could be advantageous in practical quantum tasks by optimizing the weights assigned to different measurements. Importantly, this optimization does not require quantum resources and is efficiently computable on classical computers.http://doi.org/10.1103/PhysRevResearch.6.013127 |
| spellingShingle | Shan Huang Hua-Lei Yin Zeng-Bing Chen Shengjun Wu Entropic uncertainty relations for multiple measurements assigned with biased weights Physical Review Research |
| title | Entropic uncertainty relations for multiple measurements assigned with biased weights |
| title_full | Entropic uncertainty relations for multiple measurements assigned with biased weights |
| title_fullStr | Entropic uncertainty relations for multiple measurements assigned with biased weights |
| title_full_unstemmed | Entropic uncertainty relations for multiple measurements assigned with biased weights |
| title_short | Entropic uncertainty relations for multiple measurements assigned with biased weights |
| title_sort | entropic uncertainty relations for multiple measurements assigned with biased weights |
| url | http://doi.org/10.1103/PhysRevResearch.6.013127 |
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