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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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Cite

BibTeXRIS
BibTeX
@misc{negari2026instability,
  title = {{Instability of Markov chains under infinitesimal coherent dissipation}},
  author = {Amir-Reza Negari and Yijian Zou and Timothy H. Hsieh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18983},
  eprint = {2610.18983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18983},
}
RIS
TY  - UNPB
TI  - Instability of Markov chains under infinitesimal coherent dissipation
AU  - Amir-Reza Negari
AU  - Yijian Zou
AU  - Timothy H. Hsieh
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18983
UR  - https://arxiv.org/abs/2610.18983
AB  - 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.
ER  -