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 \(\sigma\), we obtain the modified Log-Sobolev bound $\alpha_1\geq \frac{\lambda}{(2+\log\|\sigma^{-1}\|_\infty)}$ where $\lambda$ 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.

Quantum Physics (quant-ph); Functional Analysis (math.FA); Operator Algebras (math.OA)

arXiv:2609.20753 [quant-ph]

(or arXiv:2609.20753v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.20753 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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