AI 中文总结
研究量子生成模型中测量诱导过集中问题，引入三个指标诊断，证明不同监测电路输入敏感性变化，提出截断QuDDPM，数值表明其在保持性能时保留更强输入敏感性，确定测量诱导过集中是动态限制并将时间深度作为设计参数。
AI 中文摘要
量子测量是量子生成学习的关键资源，为生成多样量子样本提供内在随机性。然而，在测量辅助状态系综重采样中，重复测量会导致过集中，即不同输入状态逐渐趋向相似输出状态，抑制输入依赖的多样性。为诊断此效应，引入三个互补指标：准确性、生成能力和输入敏感性。对于哈尔随机监测电路，证明一步模型在维度抑制修正下保持输入敏感性，而顺序监测电路输入敏感性随深度损失。基于此，提出截断量子去噪扩散概率模型（QuDDPM），限制正向扩散和反向去噪过程的时间深度。数值基准表明，截断QuDDPM在保持准确性和生成能力的同时，保留更强的输入敏感性。这些结果将测量诱导过集中确定为深度监测量子生成模型的动态限制，并将时间深度确立为平衡测量诱导随机性与输入依赖多样性的设计参数。
英文摘要
Quantum measurement is a key resource for quantum generative learning, providing intrinsic stochasticity for generating diverse quantum samples. However, in measurement-assisted state-ensemble resampling, repeated measurements can also induce overconcentration: under a fixed measurement trajectory, distinct input states progressively converge toward similar output states, suppressing input-dependent diversity. To diagnose this effect, we introduce three complementary metrics: accuracy, generative power, and input sensitivity. For Haar-random monitored circuits, we prove that one-step models retain input sensitivity up to dimension-suppressed corrections, whereas sequential monitored circuits exhibit a depth-dependent loss of input sensitivity. Motivated by this diagnosis, we propose a truncated quantum denoising diffusion probabilistic model (QuDDPM), which restricts the temporal depth of both the forward diffusion and reverse denoising processes. Numerical benchmarks show that truncated QuDDPM preserves stronger input sensitivity while maintaining accuracy and generative power comparable to the original model. These results identify measurement-induced overconcentration as a dynamical limitation of deep monitored quantum generative models and establish temporal depth as a design parameter for balancing measurement-induced randomness with input-dependent diversity.
