弱退相干下混合态相仍稳定，可局部恢复。
Stability of mixed-state phases under weak decoherence
- 证明经典与交换泡利哈密顿量的吉布斯态在弱局部退相干下可逆。
- 退相干强度低于临界值时，存在局部解码器可完全逆转影响。
- 适用于高温相变点和低温有序相，对量子存储有重要意义。
我们证明了经典及交换泡利哈密顿量的吉布斯态在弱局部退相干下具有稳定性：即退相干效应可被局部逆转。特别地，结论适用于有限温度下的平衡临界点和低温有序相。这些系统中无条件时空关联为长程，局域（如梅特罗波利斯）动力学表现出临界慢化。然而，我们的结果表明，当退相干强度低于临界值时，存在局部“解码器”可消除退相干影响。这一结果意味着热稳定的量子记忆在接近临界温度时仍具有非零的退相干阈值。类似地，在扩散模型中，数据分布的稳定性意味着在生成后期存在计算高效的局部去噪器。
原文摘要 · Abstract (English)
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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