Tight Entropic Uncertainty Relations
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910187330207744 |
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| author | Riccardi, Alberto Maccone, Lorenzo |
| author_facet | Riccardi, Alberto Maccone, Lorenzo |
| contents | Entropic uncertainty relations $H(A)+H(B)\geqslant γ$ give a nonzero lower bound $γ$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $γ$ typically are state independent. Here we provide a state-independent lower bound $γ_s$ that is better than the textbook Maassen-Uffink bound and, in the limit of the parameter $s\to 2$, becomes asymptotically tight for all $A,B$. The bound can be extended to Renyi entropies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tight Entropic Uncertainty Relations Riccardi, Alberto Maccone, Lorenzo Quantum Physics Entropic uncertainty relations $H(A)+H(B)\geqslant γ$ give a nonzero lower bound $γ$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $γ$ typically are state independent. Here we provide a state-independent lower bound $γ_s$ that is better than the textbook Maassen-Uffink bound and, in the limit of the parameter $s\to 2$, becomes asymptotically tight for all $A,B$. The bound can be extended to Renyi entropies. |
| title | Tight Entropic Uncertainty Relations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.01832 |