Braess, while working on traffic modeling, noticed that traffic flow in a network can be worsened by adding extra edges to an existing network. This seemingly counterintuitive phenomenon is known as the Braess paradox. We consider a quantum network, where edges represent shared entangled states between spatially separated parties (nodes). The goal is to entangle two previously uncorrelated nodes using entanglement swappings. The amount of entanglement between the distant nodes is quantified by the average concurrence of the states established, as a result of the entanglement swappings. We then introduce an additional edge of maximally entangled Bell states in the network. We show that the introduction of the additional maximally entangled states to this network leads to lower concurrence between the two previously uncorrelated nodes. Thus we demonstrate the occurrence of a phenomenon in a quantum network that is analogous to the Braess paradox in traffic networks.

中文翻译：

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量子网络中的 Braess 悖论

Braess 在进行流量建模时注意到，在现有网络中添加额外的边可能会恶化网络中的流量。这种看似违反直觉的现象被称为布雷斯悖论。我们考虑一个量子网络，其中边代表空间分离方（节点）之间共享的纠缠状态。目标是使用纠缠交换来纠缠两个以前不相关的节点。作为纠缠交换的结果，远程节点之间的纠缠量通过所建立状态的平均并发度来量化。然后，我们在网络中引入了额外的最大纠缠贝尔态边缘。我们表明，向该网络引入额外的最大纠缠状态会导致两个先前不相关的节点之间的并发性降低。