{"ID":23620893,"CreatedAt":"2026-09-18T06:47:37.825099056Z","UpdatedAt":"2026-09-18T06:47:37.825099056Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20753","arxiv_id":"2609.20753","title":"Quantum Entropy Contraction and Factorization from Hypercontractivity","abstract":"We prove that hypercontractivity implies entropy contraction for a single quantum channel, without a detailed balance condition. For primitive quantum Markov semigroups that are KMS-symmetric with respect to a faithful invariant state \\(σ\\), we obtain the modified Log-Sobolev bound $α_1\\geq \\fracλ{(2+\\log\\|σ^{-1}\\|_\\infty)}$ where $λ$ is the spectral gap. This removes the assumption of \\(L_p\\)-regularity for the comparison through the log-Sobolev constant. As an application, we show that the hypercontractivity of an average of two conditional expectations implies the approximate tensorization of relative entropy.","short_abstract":"We prove that hypercontractivity implies entropy contraction for a single quantum channel, without a detailed balance condition. For primitive quantum Markov semigroups that are KMS-symmetric with respect to a faithful invariant state \\(σ\\), we obtain the modified Log-Sobolev bound $α_1\\geq \\fracλ{(2+\\log\\|σ^{-1}\\|_\\in...","url_abs":"https://arxiv.org/abs/2609.20753","url_pdf":"https://arxiv.org/pdf/2609.20753v1","authors":"[\"Li Gao\",\"Lijun Wang\"]","published":"2026-09-17T17:41:27Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"math.FA\",\"math.OA\"]","methods":"[]","has_code":false}