Relative entropic uncertainty relation for scalar quantum fields
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum...
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| Format: | Article |
| Language: | English |
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SciPost
2022-03-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.12.3.089 |
| _version_ | 1819104670209015808 |
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| author | Stefan Floerchinger, Tobias Haas, Markus Schröfl |
| author_facet | Stefan Floerchinger, Tobias Haas, Markus Schröfl |
| author_sort | Stefan Floerchinger, Tobias Haas, Markus Schröfl |
| collection | DOAJ |
| description | Entropic uncertainty is a well-known concept to formulate uncertainty
relations for continuous variable quantum systems with finitely many degrees of
freedom. Typically, the bounds of such relations scale with the number of
oscillator modes, preventing a straight-forward generalization to quantum field
theories. In this work, we overcome this difficulty by introducing the notion
of a functional relative entropy and show that it has a meaningful field theory
limit. We present the first entropic uncertainty relation for a scalar quantum
field theory and exemplify its behavior by considering few particle excitations
and the thermal state. Also, we show that the relation implies the
multidimensional Heisenberg uncertainty relation. |
| first_indexed | 2024-12-22T02:10:02Z |
| format | Article |
| id | doaj.art-58e6b7b6e80e46738bf94b247ae65721 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-22T02:10:02Z |
| publishDate | 2022-03-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-58e6b7b6e80e46738bf94b247ae657212022-12-21T18:42:25ZengSciPostSciPost Physics2542-46532022-03-0112308910.21468/SciPostPhys.12.3.089Relative entropic uncertainty relation for scalar quantum fieldsStefan Floerchinger, Tobias Haas, Markus SchröflEntropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum field theories. In this work, we overcome this difficulty by introducing the notion of a functional relative entropy and show that it has a meaningful field theory limit. We present the first entropic uncertainty relation for a scalar quantum field theory and exemplify its behavior by considering few particle excitations and the thermal state. Also, we show that the relation implies the multidimensional Heisenberg uncertainty relation.https://scipost.org/SciPostPhys.12.3.089 |
| spellingShingle | Stefan Floerchinger, Tobias Haas, Markus Schröfl Relative entropic uncertainty relation for scalar quantum fields SciPost Physics |
| title | Relative entropic uncertainty relation for scalar quantum fields |
| title_full | Relative entropic uncertainty relation for scalar quantum fields |
| title_fullStr | Relative entropic uncertainty relation for scalar quantum fields |
| title_full_unstemmed | Relative entropic uncertainty relation for scalar quantum fields |
| title_short | Relative entropic uncertainty relation for scalar quantum fields |
| title_sort | relative entropic uncertainty relation for scalar quantum fields |
| url | https://scipost.org/SciPostPhys.12.3.089 |
| work_keys_str_mv | AT stefanfloerchingertobiashaasmarkusschrofl relativeentropicuncertaintyrelationforscalarquantumfields |