Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups

@misc{wan2026quantum,
  title = {{Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups}},
  author = {Jincheng Wan and Jinsong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21368},
  eprint = {2609.21368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21368},
}

TY  - UNPB
TI  - Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups
AU  - Jincheng Wan
AU  - Jinsong Wu
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21368
UR  - https://arxiv.org/abs/2609.21368
AB  - In this paper, we establish a quantum Cheeger inequality for primitive KMS-symmetric quantum Markov semigroups in terms of projection conductance. We discuss both projection conductance and classical conductance for graph-based KMS-symmetric quantum Markov semigroups. We show that hypercontractivity and the logarithmic Sobolev inequality hold for primitive KMS-symmetric quantum Markov semigroups. We also present applications of the quantum Cheeger inequality to logarithmic Sobolev inequalities, hypercontractivity, and complete modified logarithmic Sobolev inequalities.
ER  -