Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups

@misc{liu2026entropy,
  title = {{Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups}},
  author = {Zhengwei Liu and Jincheng Wan and Jinsong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06201},
  eprint = {2610.06201},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06201},
}

TY  - UNPB
TI  - Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups
AU  - Zhengwei Liu
AU  - Jincheng Wan
AU  - Jinsong Wu
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06201
UR  - https://arxiv.org/abs/2610.06201
AB  - In this paper, we study finite-mode Gaussian quantum Markov semigroups with a faithful invariant Gaussian state. We present an algebraic characterization of the complete modified logarithmic Sobolev inequality relative to the fixed-point algebra, and we obtain the corresponding optimal constant under the assumption that the drift evolution e^tZ converges as t→∞. We establish hypercontractivity for such quantum Markov semigroups with Hurwitz drift, in the sense that every fixed pair 1<p<q<∞ is attained at sufficiently large times. We find that the usual reverse hypercontractive curves with a positive rate from time zero can fail in general, but every fixed pair 1/2 < p < q < 1 is attained at sufficiently large times under the Hurwitz assumption. We also systematically investigate the p-logarithmic Sobolev inequality and show that the p-logarithmic Sobolev constant can be negative for 0 < p < 1/2.
ER  -