发表机构
Rutgers University（罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明对于任意量子比特信道，中点放置纠缠源在可行性意义上优于端点放置，证实了近期猜想。
AI 中文摘要
本研究探讨了沿由两个噪声量子比特信道组成的通信线路放置纠缠源的问题。近期工作基于解析和数值论证，认为中点放置应至少与端点放置同样有利。本文证明，对于任意量子比特信道，若顺序组合能保持纠缠，则相应的并行作用不能湮灭所有纠缠。证明使用了该近期工作中引入的转置因子化判据。量子Sinkhorn缩放将每个严格正量子比特信道转换为幺正代表，幺正量子比特信道的特殊规范形式则通过原始信道产生所需的转置映射因子化。去极化正则化与纠缠破坏信道集合的封闭性将结果推广至任意信道。因此，$\Lambda_1 \otimes \Lambda_2 \in \mathrm{EA}$ 蕴含 $\Lambda_2 \circ \Lambda_1 \in \mathrm{EB}$，且通过交换两个信道，相反组合顺序亦成立。这证明了近期猜想：在最初定义最优性的可行性意义上，中点放置对所有量子比特信道均为最优。
英文摘要
This work studies the placement of an entanglement source along a communication line formed by two noisy qubit channels. Recent work argued, on analytical and numerical grounds, that midpoint placement should be at least as favorable as endpoint placement. Here it is shown that, for arbitrary qubit channels, if a sequential composition can preserve entanglement, then the corresponding parallel action cannot annihilate all entanglement. The proof uses the transpose-factorization criterion introduced in that recent work. Quantum Sinkhorn scaling converts every strictly positive qubit channel into a unital representative, and the special normal form of unital qubit channels then yields the required factorization of the transposed map through the original channel. Depolarizing regularization and the closedness of the set of entanglement-breaking channels extend the result to arbitrary channels. Consequently, $Λ_1 \otimes Λ_2 \in \mathrm{EA}$ implies $Λ_2 \circ Λ_1 \in \mathrm{EB}$, and, by exchanging the two channels, the same holds for the opposite composition order. This proves the recent conjecture that midpoint placement is optimal for all qubit channels, in the feasibility sense in which that optimality was originally defined.
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