分形量子中继网络的重正化和小世界模型
Renormalization and small-world model of fractal quantum repeater networks
摘要：
量子网络提供了量子信息交换的途径。量子网络的主要任务是在远程节点之间分发纠缠。量子中继协议虽然可以实现长距离的纠缠分发，但它仅限于一维线性网络。在这里，我们开发了一个通用的框架，允许量子中继器协议的应用到任意的量子中继器网络的分形结构。这种网络中的纠缠分布被映射到重正化。此外，我们证明了递归的重正化变换的代数次数可以触发分形到小世界的转变，从而实现可扩展的量子小世界网络。我们的结果为量子中继器理论提供了新的见解，有助于大规模量子网络的实际构建。
英文摘要：
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
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