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arXiv · 2511.01976

Stability of mixed-state phases under weak decoherence

Yifan F. Zhang·Sarang Gopalakrishnan
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Abstract

We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to finite-temperature equilibrium critical points and ordered low-temperature phases. In these systems the unconditional spatio-temporal correlations are long-range, and local (e.g., Metropolis) dynamics exhibits critical slowing down. Nevertheless, our results imply the existence of local "decoders" that undo the decoherence, when the decoherence strength is below a critical value. An implication of these results is that thermally stable quantum memories have a threshold against decoherence that remains nonzero as one approaches the critical temperature. Analogously, in diffusion models, stability of data distributions implies the existence of computationally-efficent local denoisers in the late-time generation dynamics.

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Yifan F. Zhang, Sarang Gopalakrishnan. 2025-11-03. Stability of mixed-state phases under weak decoherence. https://arxiv.org/abs/2511.01976

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