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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 α1≥ λ/((2+log|σ−1|∞)) where λ is the spectral gap. This removes the assumption of Lp-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.
Related
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BibTeX
@misc{gao2026quantum,
title = {{Quantum Entropy Contraction and Factorization from Hypercontractivity}},
author = {Li Gao and Lijun Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20753},
eprint = {2609.20753},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20753},
}
RIS
TY - UNPB
TI - Quantum Entropy Contraction and Factorization from Hypercontractivity
AU - Li Gao
AU - Lijun Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.20753
UR - https://arxiv.org/abs/2609.20753
AB - 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≥ λ/((2+log|σ^−1|_∞)) 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.
ER -