Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers

Abstract:We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time $L^2$-to-$L^p$ bound for any $p>2$.

arXiv:2610.06764 [quant-ph]

(or arXiv:2610.06764v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.06764 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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