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Quantum Algorithms
A conjecture on a tight norm inequality in the finite-dimensional l_p
arXiv
Authors: A. S. Holevo, A. V. Utkin
Year
2026
Paper ID
35741
Status
Preprint
Abstract Read
~2 min
Abstract Words
89
Citations
N/A
Abstract
We suggest a tight inequality for norms in d-dimensional space lp which has simple formulation but appears hard to prove. We give a proof for d=3 and provide a detailed numerical check for dleq 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: lp-norm, Rényi entropy, tight inequality, maximization of a convex function.
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- It adds a 2026 reference point for readers tracking recent quantum research.
- We suggest a tight inequality for norms in d-dimensional space lp which has simple formulation but appears hard to prove.
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