AI 中文总结
研究纠缠分布式一夫一妻制对量子信道模拟的限制，引入分数可扩展性，证明其相关特性，建立分布式一夫一妻制，得出擦除概率超半的量子擦除信道无法模拟噪声较小信道的结论。
AI 中文摘要
纠缠具有一夫一妻制：若在多方之间共享，任意两方间的纠缠不会很强。对于整数\(k\geq2\)，态\(\rho_{AB}\)的\(k\)可扩展性将其量化为该态的环境可模拟的\(B\)的份数。我们引入分数可扩展性，它能更精细地表征泄漏到环境中的量子关联，并证明其在张量积下不变且在局部操作下单调。我们还建立了纠缠的分布式一夫一妻制：对于\(AB_1B_2\dots B_n\)上的任意态，从\(B_i\)中\(k\leq n/2\)个系统的随机子集中提取EPR对的最大平均概率为\(k/n\)。利用这些工具，我们表明任何擦除概率超过一半的量子擦除信道都无法模拟噪声较小的擦除信道，即使使用渐近多个噪声较大的信道。
英文摘要
Entanglement is monogamous: if it is shared among more than two parties, the entanglement between any pair cannot be very strong. For an integer $k\geq 2$, $k$-extendibility of a state $ρ_{AB}$ quantifies this as the number of copies of $B$ that can be simulated by the state's environment. We introduce fractional extendibility, which gives a finer characterization of the quantum correlation that is leaked to the environment, and prove that it is invariant under tensor products and monotonic under local processing. We also establish the distributed monogamy of entanglement: for any state on $AB_1B_2\dots B_n$, the maximum average probability of extracting an EPR pair from a random subset of $k \leq n/2$ systems among the $B_i$'s is the fraction $k/n$. With these tools we resolve a conjecture posed by Matthew Hastings: any quantum erasure channel with erasure probability at least $\frac{1}{2}$ cannot simulate a less noisy erasure channel, even with asymptotically many uses of the noisier channel.
Comments6 pages, 5 pages of supplemental material, 2 figures; Proof of Hastings' conjecture on erasure channel simulation from fractional extendibility and distributed monogamy of entanglement. See arXiv:2607.17319 for an independent proof of the erasure-simulation conjecture
