信息校准量子扩散：对齐正向噪声与反向可恢复性
Information-Calibrated Quantum Diffusion: Aligning Forward Noise with Reverse Recoverability
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中文总结 AI 辅助
该研究提出信息校准量子扩散方法，引入经典-量子信息减量作为内在扩散坐标，构建结合恢复约束与分布匹配的随机学习器，在四量子比特TFIM实验中降低了Wtr指标且性能优于官方QuDDPM。
中文摘要 AI 辅助
量子扩散模型通常以原始信道强度参数化正向 corruption（噪声干扰），但参数增量相等并不意味着信息擦除量相等或诱导的逆问题具有可比性。我们引入经典-量子信息减量Δₜ=I(X:Qₜ₋₁)-I(X:Qₜ)作为带标签量子系综的内在扩散坐标。在退极化过程中，均等Δₜ可得到正向路径的唯一极小极大离散化，而通用可恢复性赋予该量操作层面的反向解释，即作为与标签无关的CPTP恢复信道可达到的期望对数保真度预算。互补连续性与成对几何逆定理为最优公共信道恢复误差提供下界。我们进一步表明，局部校准对于随机生成根本不足：即使在固定的非对易两量子比特系统中，相同的局部保真度规律与预算可行风险可共存于宏观上不同的输出分布。这促使一种结合定理规模恢复约束与分布匹配的随机学习器，我们为其建立有限样本校准与组合迹- Wasserstein控制。在四量子比特TFIM上，受控容量扩展将端点Wtr从.622降至.424（在所有10个匹配种子上），且以更少的可训练参数实现比官方QuDDPM（.498）更低的Wtr。
英文摘要
Quantum diffusion models typically parameterize forward corruption by raw channel strength, even though this parameter does not directly quantify how much ensemble information is erased or how difficult the corresponding reverse problem is. We introduce the classical--quantum information decrement $Δ_t=I(X{:}Q_{t-1})-I(X{:}Q_t)$ as an intrinsic diffusion coordinate that links forward noise allocation to reverse recoverability. Along depolarization, equalizing $Δ_t$ yields the unique minimax discretization of the forward information loss, while universal recoverability gives the same quantity an operational interpretation as a physically attainable local recovery budget. We further show that such local calibration is not sufficient for stochastic generation: models can satisfy the same recovery criterion while producing substantially different state distributions. This motivates a stochastic learner that combines information-calibrated recovery constraints with distribution matching. We establish finite-sample calibration and compositional trace-Wasserstein control for the resulting learner. Controlled quantum experiments validate the predicted information--recovery alignment, show that the recovery constraints improve local inversion, and confirm the complementary role of distribution matching in endpoint generation. The resulting framework also achieves stronger endpoint trace-Wasserstein performance than an official QuDDPM implementation with fewer trainable parameters. Overall, our work provides a unified information-theoretic principle for designing forward schedules, calibrating reverse steps, and separating physical recovery from generative coverage in quantum diffusion.
