AI 中文总结
研究超出正部分转置（PPT）设置的映射复合问题，针对三量子比特完全正定映射，证明特定条件下映射复合是纠缠破缺的，确定1-不可蒸馏CP映射锥的性质，还证明特定态在任意选择性测量下不能产生终端纠缠。
AI 中文摘要
纠缠交换是量子中继器中用于在远距离方之间建立纠缠的基本操作。正部分转置（PPT）平方猜想询问两个PPT纠缠链路是否能通过纠缠交换产生终端纠缠，或者等价地，两个PPT映射的复合是否总是纠缠破缺的。受此猜想启发，我们研究了超出PPT设置的映射复合问题。对于三量子比特完全正定（CP）映射，我们证明了任何其蔡矩阵是1-不可蒸馏的CP映射与任何其蔡矩阵施密特数至多为2的CP映射的复合，无论顺序如何都是纠缠破缺的。此外，我们表明1-不可蒸馏CP映射的锥恰好是最大的三量子比特CP映射锥，其与每个蔡矩阵施密特数至多为2的CP映射的复合在两个顺序上都是纠缠破缺的。最后，尽管映射复合仅捕获纠缠交换中的标准最大纠缠结果，但我们证明了在中间系统上的任意选择性测量下，任何1-不可蒸馏的双三量子比特态和任何施密特数至多为2的态都不能产生终端纠缠。
英文摘要
Entanglement swapping is a fundamental operation in quantum repeaters for establishing entanglement between distant parties. The positive partial transpose (PPT) squared conjecture asks whether two PPT entangled links can generate terminal entanglement through entanglement swapping, or equivalently, whether the composition of two PPT maps is always entanglement breaking. Motivated by this conjecture, we investigate the map-composition problem beyond the PPT setting. For qutrit completely positive (CP) maps, we prove that the composition of any CP map whose Choi matrix is $1$-undistillable with any CP map whose Choi matrix has Schmidt number at most two is entanglement breaking in either order. Moreover, we show that the cone of $1$-undistillable CP maps is exactly the largest qutrit cone of CP maps whose composition with every CP map whose Choi matrix has Schmidt number at most two is entanglement breaking in both orders. Finally, although map composition captures only the standard maximally entangled outcome in entanglement swapping, we prove that any $1$-undistillable two-qutrit state and any state of Schmidt number at most two cannot generate terminal entanglement under an arbitrary selective measurement on the intermediate systems.
Comments9 pages, 3 figures
