A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature

• URL: http://arxiv.org/abs/2510.08542v1
• Date: Thu, 09 Oct 2025 17:54:41 GMT
• Title: A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
• Authors: Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang,
• Abstract summary: A central challenge in quantum physics is to understand the structural properties of many-body systems.<n>For classical systems, we have a unified perspective which connects structural properties of systems at thermal equilibrium to the Markov chain dynamics that mix to them.<n>We develop a general framework that brings the breadth and flexibility of the classical theory to quantum Gibbs states at high temperature.
• Score: 17.858283119788357
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A central challenge in quantum physics is to understand the structural properties of many-body systems, both in equilibrium and out of equilibrium. For classical systems, we have a unified perspective which connects structural properties of systems at thermal equilibrium to the Markov chain dynamics that mix to them. We lack such a perspective for quantum systems: there is no framework to translate the quantitative convergence of the Markovian evolution into strong structural consequences. We develop a general framework that brings the breadth and flexibility of the classical theory to quantum Gibbs states at high temperature. At its core is a natural quantum analog of a Dobrushin condition; whenever this condition holds, a concise path-coupling argument proves rapid mixing for the corresponding Markovian evolution. The same machinery bridges dynamic and structural properties: rapid mixing yields exponential decay of conditional mutual information (CMI) without restrictions on the size of the probed subsystems, resolving a central question in the theory of open quantum systems. Our key technical insight is an optimal transport viewpoint which couples quantum dynamics to a linear differential equation, enabling precise control over how local deviations from equilibrium propagate to distant sites.

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