AI 中文总结
受Werner态可蒸馏性偏迹公式启发，证明秩至多为二矩阵的二分偏迹不等式，应用于证明NPT Werner态双拷贝不可蒸馏性等，还解决了相关奇异值最大化问题及证明了矩阵不等式双参数扩展。
AI 中文摘要
受Werner态可蒸馏性的等效偏迹公式启发，我们证明了对于每个秩至多为二的矩阵的二分偏迹不等式。作为应用，我们证明了任意局部维度下NPT Werner态的双拷贝不可蒸馏性，解决了相关开放问题。我们还证明了矩阵不等式的双参数扩展，并表明两个单独的单拷贝不可蒸馏的NPT Werner态不能相互激活单拷贝可蒸馏性。我们还解决了与双四元数情况相关的奇异值最大化问题。
英文摘要
Motivated by the equivalent partial-trace formulations of Werner-state distillability [P. Costa Rico, Lett. Math. Phys. 115, 47 (2025); S.-Y. Qi et al., Phys. Rev. A 110, 012406 (2024)], we prove a bipartite partial-trace inequality for every matrix of rank at most two. As applications, we prove the two-copy undistillability of NPT Werner states in arbitrary local dimension, thereby resolving this open problem highlighted in [P. Horodecki et al., PRX Quantum 3, 010101 (2022)]. We further prove a two-parameter extension of the matrix inequality and show that two individually one-copy-undistillable NPT Werner states cannot activate each other's one-copy distillability. We also resolve the singular-value maximization problem associated with the two-ququart case.
Comments9 pages, no figures. The proof of the main result, namely Theorem 5, was completed in June 2026, and the remaining results and manuscript were finalized in the following month
