量子扩散模型反向过程存在不可消除的噪声极限。
Score Reversal Is Not Free for Quantum Diffusion Models
- 提出量子反向扩散的精确物理定律，揭示噪声与压缩度的临界关系。
- 在纯损耗模型下，反向过程最小噪声代价可闭式表达，超过临界值则无法避免噪声。
- 适用于多模系统，且纯态反向过程在时间上发散，动态不可达。
经典反向扩散通过固定噪声下的漂移变化实现。我们发现量子版本遵循精确规律，并具有明确相变边界。对于连续变量退相干的标准模型——高斯纯损耗动力学，证明了无限制瞬时反向最优解存在从无噪声到有噪声的相变：当压缩比低于临界值时，反向可无噪声；高于该值时，完全正性要求导致不可避免的反向噪声，其最小代价可闭式求解。最优反向扩散唯一地与协方差对齐，同时最小化几何、计量和热力学代价。在多模轨迹中，总代价在一组规范模式分辨数据上可加，全局连续协议可在每个混合态区间达到此最优。若包含纯非经典终点，则对任意 t>0，相同点态规律成立，但最优解随 2/t 发散：纯量子态的精确高斯反向在动力学上不可实现。这些结果确立了量子反向扩散理论的精确高斯基准。
原文摘要 · Abstract (English)
Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted instantaneous reverse optimum exhibits a noiseless-to-noisy transition: below a critical squeezing-to-thermal ratio, reversal can be noiseless; above it, complete positivity forces irreducible reverse noise whose minimum cost we determine in closed form. The optimal reverse diffusion is uniquely covariance-aligned and simultaneously minimizes the geometric, metrological, and thermodynamic price of reversal. For multimode trajectories, the exact cost is additive in a canonical set of mode-resolved data, and a globally continuous protocol attains this optimum on every mixed-state interval. If a pure nonclassical endpoint is included, the same pointwise law holds for every $t>0$, but the optimum diverges as $2/t$: exact Gaussian reversal of a pure quantum state is dynamically unattainable. These results establish the exact Gaussian benchmark against which any broader theory of quantum reverse diffusion must be measured.
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