Stability of mixed-state phases under weak decoherence

TL;DR

This paper proves that Gibbs states of classical and commuting-Pauli Hamiltonians remain stable under weak local decoherence, allowing local correction of decoherence effects even near critical points, with implications for quantum memories and data denoising.

Contribution

It demonstrates the local reversibility of decoherence effects in Gibbs states of certain Hamiltonians, extending stability results to critical and low-temperature phases.

Findings

Decoherence effects can be locally reversed below a critical strength.

Thermally stable quantum memories have a nonzero decoherence threshold near critical temperature.

Existence of efficient local denoisers in diffusion models for data stability.

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.