A conjecture on a tight norm inequality in the finite-dimensional l_p

2026/03/25 by A. S. Holevo, A. V. Utkin
#quant-ph #math-ph #math.FA #math.MP

paper · pdf

Abstract

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≤ 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.

Citations

• Quantum accessible information and classical entropy inequalities

Related

• A remainder term for Hölder's inequality for matrices and quantum entropy inequalities
• L^p-norm inequality using q-moment and its applications
• L^p spaces of operator-valued functions
• Tight entropy bound based on p-quasinorms
• CB-norm estimates for maps between noncommutative L_p-spaces and quantum channel theory