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arXiv · 2609.21368

Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups

Jincheng Wan·Jinsong Wu
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Abstract

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.

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BibTeXRIS

Jincheng Wan, Jinsong Wu. 2026-09-18. Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups. https://arxiv.org/abs/2609.21368

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