Instability of Markov chains under infinitesimal coherent dissipation

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.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2610.18983 [quant-ph]

(or arXiv:2610.18983v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.18983 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.