Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers

@misc{chen2026sizeindependent,
  title = {{Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers}},
  author = {Hongrui Chen and Zhiyan Ding and Jianfeng Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31571},
  eprint = {2610.31571},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31571},
}

TY  - UNPB
TI  - Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers
AU  - Hongrui Chen
AU  - Zhiyan Ding
AU  - Jianfeng Lu
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31571
UR  - https://arxiv.org/abs/2610.31571
AB  - We propose a new method for proving L^2 and modified logarithmic Sobolev inequalities with constants independent of system size for quantum Gibbs samplers whose Lindblad generators satisfy Kubo-Martin-Schwinger (KMS) detailed balance. We first establish the L^2 logarithmic Sobolev inequality by transporting it along a temperature-dependent path from the infinite-temperature product state to the target Gibbs state while maintaining a size-independent decay rate for the sandwiched Rényi-2 divergence. A tensor-power argument, combined with the quantum asymptotic equipartition property, then transfers this decay bound to relative entropy, yielding the modified logarithmic Sobolev inequality. This approach provides a general framework for proving size-independent logarithmic Sobolev inequalities for quantum Gibbs samplers. We apply it to two regimes: one-dimensional quantum spin chains at every finite temperature, and finite-range quantum spin systems at sufficiently high temperature in any fixed dimension.
ER  -