Quantum Reverse Hypercontractivity for KMS-Symmetric Quantum Markov Semigroups
Abstract
In this paper, we construct primitive KMS-symmetric quantum Markov semigroups for which the p-logarithmic Sobolev constant vanishes at p=1/2 and a correlated graph-based example for which the p-logarithmic Sobolev constant tends to −∞ as p→ 0+. These examples obstruct a positive uniform reverse-hypercontractivity rate on (0,1). By contrast, we show that every primitive KMS-symmetric quantum Markov semigroup satisfies quantum reverse hypercontractivity for 1/2< p≤ q < 1 with explicit sufficient times. For each fixed δ>0, a sufficiently strong dephasing perturbation satisfies a uniform positive logarithmic Sobolev inequality on $[δ, 1]$ and hence quantum reverse hypercontractivity for δ< p≤ q<1 with fixed 0<δ<1/2. Furthermore, we establish reverse hypercontractivity for graph-based KMS-symmetric quantum Markov semigroups for δ< p≤ q< 1 with fixed 0<δ<1 for connected graphs when n ≥ 3.
Related
- Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups
- Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups
- Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups
- The Differential Structure of Generators of KMS-Symmetric Quantum Markov Semigroups
- Quantum Entropy Contraction and Factorization from Hypercontractivity
BibTeX
@misc{wu2026quantum,
title = {{Quantum Reverse Hypercontractivity for KMS-Symmetric Quantum Markov Semigroups}},
author = {Jinsong Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00242},
eprint = {2610.00242},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00242},
}
RIS
TY - UNPB
TI - Quantum Reverse Hypercontractivity for KMS-Symmetric Quantum Markov Semigroups
AU - Jinsong Wu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00242
UR - https://arxiv.org/abs/2610.00242
AB - In this paper, we construct primitive KMS-symmetric quantum Markov semigroups for which the p-logarithmic Sobolev constant vanishes at p=1/2 and a correlated graph-based example for which the p-logarithmic Sobolev constant tends to −∞ as p→ 0^+. These examples obstruct a positive uniform reverse-hypercontractivity rate on (0,1). By contrast, we show that every primitive KMS-symmetric quantum Markov semigroup satisfies quantum reverse hypercontractivity for 1/2< p≤ q < 1 with explicit sufficient times. For each fixed δ>0, a sufficiently strong dephasing perturbation satisfies a uniform positive logarithmic Sobolev inequality on $[δ, 1]$ and hence quantum reverse hypercontractivity for δ< p≤ q<1 with fixed 0<δ<1/2. Furthermore, we establish reverse hypercontractivity for graph-based KMS-symmetric quantum Markov semigroups for δ< p≤ q< 1 with fixed 0<δ<1 for connected graphs when n ≥ 3.
ER -