完全不可分性与有限模高斯态的真正多体纠缠等价

中文摘要 AI 辅助

对于一般混合态，跨越每个二分态的纠缠并不必然意味着真正多体纠缠（GME），因为双可分分解可能逐项切换可分离割。我们证明，对于有限多个玻色子模的高斯态，这种凸性歧义消失。更一般地，对于任何有限分态族，由跨越这些分态可分离的态生成的迹范数闭凸类中的高斯密度算符，已经在该族中一个固定分态上可分离。只有目标态是高斯态；有效分解可以是连续的，并且可以包含任意非高斯态。因此，完全不可分性与GME重合，高斯k-可分性和k-可产生性简化为固定分态测试，并且逐方张量幂不能从双可分高斯态激活GME。证明结合了谱选择器与全纯刚性论证，该论证将高斯态平方根范围内的一个乘积向量转换为块局部协方差证书。结果表明，分态混合（一种通用的混合态机制）不会增加新的精确有限模高斯态。

英文摘要

For general mixed states, entanglement across every bipartition need not imply genuine multipartite entanglement (GME), because a biseparable decomposition may switch the separable cut from term to term. We prove that this convex ambiguity disappears for Gaussian states of finitely many bosonic modes. More generally, for any finite family of partitions, a Gaussian density operator in the trace-norm-closed convex class generated by states separable across those partitions is already separable across one fixed partition in the family. Only the target is Gaussian; a valid decomposition may be continuous and may contain arbitrary non-Gaussian states. Thus full inseparability and GME coincide, Gaussian k-separability and k-producibility reduce to fixed-partition tests, and party-wise tensor powers cannot activate GME from a biseparable Gaussian state. The proof combines a spectral selector with a holomorphic rigidity argument that converts one product vector in the square-root range of a Gaussian state into a block-local covariance certificate. The result shows that partition mixing, a generic mixed-state mechanism, adds no new exact finite-mode Gaussian states.

发表机构

• School of Applied Science, Beijing Information Science and Technology University（北京信息科技大学应用科学学院）
• School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University（北京信息科技大学仪器科学与光电工程学院）
• School of Physics, Beihang University（北京航空航天大学物理学院）
• Jiangxi Beidouyun Intelligent Technology Co. Ltd.（江西北斗云智能科技有限公司）
• School of Automation (School of Artificial Intelligence), Beijing Information Science and Technology University（北京信息科技大学自动化学院（人工智能学院））
• School of Space and Earth Sciences, Beihang University（北京航空航天大学空间与地球科学学院）

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