{"ID":2846841,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01976","arxiv_id":"2511.01976","title":"Stability of mixed-state phases under weak decoherence","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.","short_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...","url_abs":"https://arxiv.org/abs/2511.01976","url_pdf":"https://arxiv.org/pdf/2511.01976v1","authors":"[\"Yifan F. Zhang\",\"Sarang Gopalakrishnan\"]","published":"2025-11-03T19:00:02Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cond-mat.stat-mech\",\"cs.LG\",\"math-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}