Strong entanglement distribution of quantum networks
Xue Yang, Yan‐Han Yang, Ming‐Xing Luo
Abstract
Large-scale quantum networks have been employed to overcome practical constraints of transmission and storage for single entangled systems. Our goal in this paper is to explore the strong entanglement distribution of quantum networks. We firstly show that any connected network consisting of generalized Einstein-Podolsky-Rosen states and Greenberger-Horne-Zeilinger states satisfies the strong Coffman-Kundu-Wootters monogamy inequality in terms of the bipartite entanglement measure; in addition, the monogamy inequalities are also considered for generic entangled quantum networks. This reveals the interesting feature of high-dimensional entanglement with local tensor decomposition going beyond qubit entanglement. We then apply the entanglement distribution relation in entangled networks to get a quantum maximum-flow minimum-cut theorem in terms of von Neumann entropy and R\'enyi-$\ensuremath{\alpha}$ entropy. We finally classify entangled quantum networks by distinguishing network configurations under local unitary operations. These results provide insights into characterizing quantum networks in quantum information processing.