On Wigdersons' approach to the uncertainty principle
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909596186050560 |
|---|---|
| author | Dias, Nuno Costa Luef, Franz Prata, João Nuno |
| author_facet | Dias, Nuno Costa Luef, Franz Prata, João Nuno |
| contents | We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17438 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Wigdersons' approach to the uncertainty principle Dias, Nuno Costa Luef, Franz Prata, João Nuno Functional Analysis Mathematical Physics Quantum Physics We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles. |
| title | On Wigdersons' approach to the uncertainty principle |
| topic | Functional Analysis Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2312.17438 |