AI 中文总结
该研究针对量子信息中部分转置负性纠缠是否不可蒸馏的问题，采用Sharp维度无关不等式等方法，证明了三份Werner蒸馏端点的非负性，确立了相关常数与秩限制的最优性。
AI 中文摘要
部分转置负性纠缠是否仍不可蒸馏是量子信息理论中的长期问题。我们针对互补部分迹采用Sharp维度无关不等式，针对正交三分向量采用最优外平方不等式，分析首个未解决的三份Werner端点。后者将局部SWAP宇称统计与可分解Plucker二重向量的度量数据关联，结合这些不等式证明任意有限局域维度中，每个正半定秩二系数算子及完整正规秩二区的端点非负性。对于真正非正规算子，精确交叉格拉姆判据证明，当一个局域输出-输入支撑重叠至多为2（包括所有含量子比特大小因子的系统）且任一支撑平面包含乘积射线时，端点非负性。明确的反态与秩边界族确立了常数和秩限制的最优性。
英文摘要
Whether negative-partial-transpose entanglement can remain undistillable is a longstanding problem in quantum information theory. We analyze the first unresolved three-copy Werner endpoint using a sharp dimension-free inequality for complementary partial traces and an optimal exterior-square inequality for orthonormal tripartite vectors. The latter identifies local SWAP- parity statistics with metric data of a decomposable Plucker bivector. Together these inequalities prove endpoint nonnegativity for every positive semidefinite rank-two coefficient operator and for the complete normal rank-two sector in arbitrary finite local dimensions. For genuinely nonnormal operators, an exact crossed-Gram criterion proves nonnegativity when one local outpu-input support overlap is at most two, including every system with a qubit-sized factor, and when either support plane contains a product ray. Explicit anti-state and rank-boundary families establish optimality of the constants and the rank restriction.
