AI 中文总结
该研究针对多模量子过程学习难题，确立玻色幺正学习可处理边界，提出两类非高斯族可高效学习的前向协议，揭示学习复杂性源于非高斯性与纠缠的不可约混合。
AI 中文摘要
多模量子过程通常难以学习，原因在于其维度大且存在超出高斯类的复杂纠缠结构。本文指出根本障碍并非非高斯性本身，而是不可约多模非高斯关联的累积。我们确立了玻色幺正学习的可处理边界：输入每模能量最多为E的一般m模幺正算符，至少需要Ω(E^(2m))次信道使用；而两类广泛的非高斯族——t掺杂高斯幺正算符和高斯可纠缠幺正算符——可通过与m成多项式关系的资源完成学习，后者兼具广延非高斯性与强多模纠缠。我们的仅前向协议使用相干态探针、高斯操作、本地外差检测及经典后处理，以识别全局高斯混合并将剩余任务简化为单模或少模学习。分析还得出多模量子Darmois–Skitovich定理，表明扩模无源网络仅对高斯输入态保持乘积结构；非高斯过程的几乎必然激活定理，显示非高斯幺正算符对几乎所有相干输入态产生非高斯输出；以及从未校准相干探针学习幺正算符的方法。我们的结果表明，学习的复杂性源于非高斯性与纠缠的不可约混合，而非单独任一资源。
英文摘要
Multimode quantum processes are generally difficult to learn, due to the large dimensionality and complex entanglement structure beyond the Gaussian class. Here, we show that the fundamental obstruction is not non-Gaussianity itself, but the buildup of irreducible multimode non-Gaussian correlations. We establish a tractability frontier for bosonic unitary learning: a general $m$-mode unitary with input energy at most $E$ per mode requires at least $Ω(E^{2m})$ channel uses, whereas two broad non-Gaussian families---$t$-doped Gaussian unitaries and Gaussian-entanglable unitaries---can be learned with resources polynomial in $m$. The latter can exhibit both extensive non-Gaussianity and strong multimode entanglement. Our forward-only protocols use coherent-state probes, Gaussian operations, local heterodyne detection, and classical post-processing to identify the global Gaussian mixing and reduce the remaining task to single- or few-mode learning. The analysis also yields a multimode quantum Darmois--Skitovich theorem showing that mode-spreading passive networks preserve product structure only for Gaussian input states, an almost-sure activation theorem for non-Gaussian processes showing that non-Gaussian unitaries yield non-Gaussian outputs for almost all coherent input states, and a method for learning unitaries from uncalibrated coherent probes. Our results identify that complexity of learning arises from irreducible mixing of non-Gaussianity and entanglement, rather than either resource alone.
