论文标题
从$ n $ - 组成的资源状态生成$ k $ epr-pairs
Generating $k$ EPR-pairs from an $n$-party resource state
论文作者
论文摘要
由量子网络应用程序通过经典渠道激励，我们启动了$ n $ - 零件资源状态的研究，其中LOCC协议可以在任何$ k $ discoint of the Party otarty的各方之间创建EPR-pairs。我们提供了此类状态的构造，即$ k $距离最佳$ n/2 $不太遥远，而各方只需要持有恒定数量的Qubits。在每个方仅持有一个Qubit的特殊情况下，我们描述了一个基于Reed-Muller代码的$ K $ $ K $的家庭，其$ K $与$ \ log n $成比例，以及小数字发现$ k = 2 $和$ k = 3 $的小数字示例。我们还证明了一些下限，例如，如果$ k = n/2 $，那么当事方必须至少具有$ω（\ log \ log \ log n）$ qubits。
Motivated by quantum network applications over classical channels, we initiate the study of $n$-party resource states from which LOCC protocols can create EPR-pairs between any $k$ disjoint pairs of parties. We give constructions of such states where $k$ is not too far from the optimal $n/2$ while the individual parties need to hold only a constant number of qubits. In the special case when each party holds only one qubit, we describe a family of $n$-qubit states with $k$ proportional to $\log n$ based on Reed-Muller codes, as well as small numerically found examples for $k=2$ and $k=3$. We also prove some lower bounds, for example showing that if $k=n/2$ then the parties must have at least $Ω(\log\log n)$ qubits each.
