The entanglement entropy (EE) of any bipartition of a pure state can be approximately expressed as a sum of entanglement links (ELs). In this work, we introduce their exact extension, i.e. the entanglement hyperlinks (EHLs), a type of generalized mutual informations defined through the inclusion-exclusion principle, each of which captures contributions to the multipartite entanglement that are not reducible to lower-order terms. We show that any EHL crossing a factorized partition must vanish, and that the EHLs between any set of blocks can be expressed as a sum of all the EHLs that join all of them. This last result allows us to provide an exact representation of the EE of any block of a pure state, from the sum of the EHLs which cross its boundary. In order to illustrate their rich structure, we discuss some explicit numerical examples using ground states of local Hamiltonians. The EHLs thus provide a remarkable tool to characterize multipartite entanglement in quantum information theory and quantum many-body physics.

翻译：纯态任意二分划的纠缠熵（EE）可近似表示为纠缠链接（ELs）之和。本文中，我们引入其精确扩展——纠缠超链接（EHLs），这是一类通过容斥原理定义的广义互信息，其中每个EHL捕获了多体纠缠中不可约化为低阶项的贡献。我们证明跨越因子化分划的任何EHL必为零，且任意区块组间的EHL可表示为连接所有这些区块的全部EHL之和。后一结论使我们能够通过跨越区块边界的EHL之和，给出纯态任意区块EE的精确表示。为阐明其丰富结构，我们使用局域哈密顿量基态讨论了若干数值算例。因此，EHL为量子信息论和量子多体物理中的多体纠缠表征提供了重要工具。