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Quantum State Preparation Representation

Generalized Poincaré inequality for quantum Markov semigroups

arXiv
Authors: Marius Junge, Jia Wang

Year

2026

Paper ID

4022

Status

Preprint

Abstract Read

~2 min

Abstract Words

91

Citations

N/A

Abstract

We prove a noncommutative (p,p)-Poincaré inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our argument uses Markov dilations to obtain chain-rule estimates for Dirichlet forms and employs amalgamated free products to define an appropriate noncommutative derivation. We further generalize the argument to non-tracial σ-finite von Neumann algebras under the weaker assumption of GNS-detailed balance, using Haagerup's reduction and Kosaki's interpolation theorem. As applications, we recover noncommutative Khintchine and sub-exponential concentration inequalities.

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  • This paper contributes to the Quantum State Preparation & Representation research area in the Quantum Articles archive.
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  • We prove a noncommutative (p,p)-Poincaré inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.06005 [2] arXiv https://arxiv.org/abs/2601.06005 [3] Publisher https://arxiv.org/abs/2601.06005

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