发表机构
Indian Institute of Science Education & Research Mohali（印度科学教育研究所穆哈利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对量子边际问题，用半定规划分析四量子比特SLOCC纠缠类的可重建性，训练神经网络实现边际可重建性分类及高保真度的全局量子态重建，经实验验证有效。
AI 中文摘要
不同的局域关联集并不等价：部分约化数据片段可唯一确定全局量子态，而另一些则使其模糊。量子边际问题旨在探究一组约化密度矩阵是否能唯一确定兼容的全局量子态。尽管一般量子态可由合适的边际集唯一指定，但不同边际集的信息含量并不相同：部分可唯一确定全局态，另一些则无法确定。判断何时存在唯一性、从部分信息重建全局态，仍是计算量大且实验上具有挑战性的问题。我们发现，四量子比特系统中的多体纠缠类与可重建性信息，被紧凑编码在少量两体和三体边际中。通过半定规划，我们绘制了49种不等价SLOCC纠缠类的可重建性图谱，表明唯一性强烈依赖于纠缠结构与边际顺序。仅在约化密度矩阵上训练的神经网络可直接学习该结构，能准确对边际可重建性进行分类；当存在唯一性时，可从两体和三体边际以高保真度重建完整四量子比特密度矩阵。我们在四量子比特核磁共振量子处理器上对该方法进行基准测试，结果表明，即使存在相位阻尼和控制缺陷，从实验测量的边际得到的重建结果仍保持忠实。我们的结果显示，神经网络可学习局域关联何时能唯一指定全局量子态，并揭示了全局量子结构如何编码在约化数据中。
英文摘要
Different sets of local correlations are not equivalent: some fragments of reduced data uniquely determine a global quantum state, while others leave it ambiguous. The quantum marginal problem asks whether a collection of reduced density matrices uniquely determines a compatible global quantum state. Although generic quantum states are uniquely specified by suitable sets of marginals, different collections of marginals are not equally informative: some uniquely determine the global state, whereas others leave it ambiguous. Identifying when uniqueness holds, and reconstructing the global state from partial information, remains computationally demanding and experimentally challenging. We show that information about the multipartite entanglement class and reconstructability in four-qubit systems is compactly encoded in small sets of two- and three-qubit marginals. Using semidefinite programming, we chart the reconstructability landscape across 49 inequivalent SLOCC entanglement classes and show that uniqueness strongly depends on both entanglement structure and marginal order. Neural networks trained only on reduced density matrices learn this structure directly. They accurately classify marginal reconstructability and, when uniqueness holds, reconstruct the full four-qubit density matrix with high fidelity from two- and three-qubit marginals. We benchmark the approach on a four-qubit nuclear magnetic resonance quantum processor and demonstrate that reconstructions from experimentally measured marginals remain faithful despite phase damping and control imperfections. Our results show that neural networks can learn when local correlations uniquely specify a global quantum state, and reveal how global quantum structure is encoded in reduced data.
Comments13 pages, 11 figures
