A conjecture on a tight norm inequality in the finite-dimensional l_p
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908948934688768 |
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| author | Holevo, A. S. Utkin, A. V. |
| author_facet | Holevo, A. S. Utkin, A. V. |
| contents | We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We conclude with a brief survey of solutions for kin problems which anyhow concern minimization of the output entropy of certain quantum channel and rely upon the symmetry properties of the problem.
Key words and phrases: $l_p $-norm, Rényi entropy, tight inequality, maximization of a convex function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A conjecture on a tight norm inequality in the finite-dimensional l_p Holevo, A. S. Utkin, A. V. Quantum Physics Mathematical Physics Functional Analysis We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We conclude with a brief survey of solutions for kin problems which anyhow concern minimization of the output entropy of certain quantum channel and rely upon the symmetry properties of the problem. Key words and phrases: $l_p $-norm, Rényi entropy, tight inequality, maximization of a convex function. |
| title | A conjecture on a tight norm inequality in the finite-dimensional l_p |
| topic | Quantum Physics Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2603.24017 |