Stability of mixed-state phases under weak decoherence
This addresses the problem of decoherence stability in quantum systems for researchers in quantum information and statistical physics, offering foundational insights with potential applications in quantum memory and diffusion models.
The paper proves that Gibbs states of classical and commuting-Pauli Hamiltonians are stable under weak local decoherence, showing the effect can be locally reversed, with implications for thermally stable quantum memories having a nonzero threshold against decoherence near critical temperatures.
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.