Instability of Markov chains under infinitesimal coherent dissipation

Amir-Reza Negari; Yijian Zou; Timothy H. Hsieh

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arXiv · 2610.18983

Instability of Markov chains under infinitesimal coherent dissipation

Amir-Reza Negari·Yijian Zou·Timothy H. Hsieh

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Abstract

Under local Lindbladian evolution, the growth of conditional mutual information and its associated Markov length scale is not limited by Lieb-Robinson bounds, yet it has been unclear how quickly the Markov length can increase. We show that an arbitrarily short, strictly local Lindbladian can generate infinite Markov length from a product state. We also construct strictly local Lindbladians that converge rapidly to steady states with algebraically decaying conditional mutual information. Despite their long-range conditional correlations, the states we construct are local reversibly connected to a product state by sublinear depth circuits. Thus infinite Markov length does not imply slow relaxation nor obstruct phase stability when suitably defined.

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Amir-Reza Negari, Yijian Zou, Timothy H. Hsieh. 2026-10-13. Instability of Markov chains under infinitesimal coherent dissipation. https://arxiv.org/abs/2610.18983

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