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math.OA2026
Sharp Complete Modified Log-Sobolev Inequalities on Classical and Quantum Tori
Long Zhao
We prove that the heat semigroup on the circle has optimal complete modified logarithmic Sobolev constant \(1\). The proof is based on a matrix-valued Wirtinger inequality and yiel…
quant-ph2026
Tight Entropy Contraction of Generalized Quantum Depolarization
Li Gao, Long Zhao
We establish upper and lower bounds for relative entropy contraction of generalized quantum depolarizing channels and semigroups. Our bound provides tight first order asymptotic of…