2026-10-21 · arXiv Quantum Physics
arXiv:2610.28600v1 Announce Type: new
Abstract: We prove a complete modified logarithmic Sobolev inequality with a system-size-independent constant for Chen--Kastoryano--Gily\'en Gibbs samplers on one-dimensional spin chain at every fixed positive temperature. The result holds for Hamiltonians with bounded finite-range interactions, including noncommuting and spatially nonuniform interactions. It yields trace and diamond mixing times of order $O(\log N+\log(1/\epsilon))$. The proof establishes complete spatial entropy factorization and absorbs quasi-local errors as conditional relative entropy at the original joint state and reference. The static estimate also yields a system-size-independent CMLSI for the single-site Petz heat-bath and regularised heat-bath dynamics.
原文链接：https://arxiv.org/abs/2610.28600
查看更多资讯请见 AI 行业资讯。