发表机构
IT:U Interdisciplinary Transformation University; University of Vienna（IT:U 跨学科转型大学; 维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对两类贝尔对角态，通过凸多面体分析等方法，证明了两类中均无纠缠APPT态，给出了可分性的谱不等式判据，但未解决APPT与绝对可分性是否一致的问题。
AI 中文摘要
绝对正部分转置（APPT）态是指在任意全局幺正变换下仍保持部分转置正（PPT）的量子态，它是绝对可分态的谱松弛概念，而绝对可分态是在任意此类变换下都保持可分的量子态。尽管已有大量研究进展，但在量子比特-量子高维系统之外，这两个概念是否一致仍未得到解决，这促使人们研究结构化的态族，以便能精确分析APPT谱约束与可分性。我们在两种场景下研究贝尔对角态的该问题：标准的两量子三态（two-qutrit）外尔-海森堡（Weyl-Heisenberg）基，以及由两量子比特泡利（Pauli）算子生成的两量子四态（two-ququart）格点基。在两量子三态场景中，我们证明APPT的线性化必要条件定义了一个谱多面体，其中每个关联的外尔-海森堡贝尔对角态都可分解为显式可分态，这得到了一个可分性判据，其适用范围甚至大于APPT集合本身。在两量子四态格点贝尔对角态场景中，我们证明，一个态在其所有贝尔系数的任意置换下仍保持PPT，当且仅当它的六个最大贝尔系数之和至多为1/2，且我们证明所有此类态都是可分的；等价地，每个纠缠的格点贝尔对角态在经过适当的系数置换后会变为部分转置负（NPT）态，因此不是APPT态。这些证明结合了凸多面体分析、仿射与辛轨道约化，以及基于仿射拉格朗日子集的可分态的精确有理分解。我们的结果排除了这两类贝尔对角态族中的纠缠APPT态，并为两种场景提供了简单的谱不等式作为可分性的充分判据；不过，由于这些结果依赖于特定基，它们本身并未解决APPT与绝对可分性是否一致的问题。
英文摘要
Absolutely positive partial transpose (APPT) states, which remain PPT under every global unitary, provide a spectral relaxation of absolutely separable states, which remain separable under every such transformation. Despite substantial progress, whether these two notions coincide beyond qubit-qudit systems remains unresolved, motivating the study of structured state families in which the APPT spectral constraints and separability can be analyzed exactly. We study this problem for Bell-diagonal states in two settings: the standard two-qutrit Weyl-Heisenberg basis and the two-ququart lattice basis generated by two-qubit Pauli operators. In the two-qutrit case, we show that a linearized necessary condition for APPT defines a polytope of spectra in which every associated Weyl-Heisenberg Bell-diagonal state admits an exact decomposition into explicitly separable states. This yields a separability criterion that applies to a region even larger than the APPT set itself. In the two-ququart lattice Bell-diagonal setting, we show that a state remains PPT under every permutation of its Bell coefficients if and only if its six largest Bell coefficients sum to at most 1/2, and we prove that all such states are separable. Equivalently, every entangled lattice Bell-diagonal state becomes NPT after a suitable coefficient permutation and is therefore not APPT. The proofs combine convex-polytope analysis, affine and symplectic orbit reductions, and exact rational decompositions into separable states supported on affine Lagrangian subsets. Our results rule out entangled APPT states in both Bell-diagonal families, and provide simple spectral inequalities as sufficient criteria for separability in both cases. Being basis-specific, however, they do not by themselves settle whether APPT and absolute separability coincide.
Comments13 + 9 pages, no figures
