Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to have the property of strong nonlocality if it is locally irreducible for every bipartition of the subsystems. Most of the known results are limited to sets with product states. Shi et al. presented the first result of strongly nonlocal sets with entanglement [Phys. Rev. A 102, 042202 (2020)], and they questioned the existence of a strongly nonlocal set with genuine entanglement. In this work, we relate the strong nonlocality of some special set of genuine entanglement to the connectivities of some graphs. Using this relation, we successfully construct sets of genuinely entangled states with strong nonlocality. As a consequence, our constructions give a negative answer to Shi et al.'s question and also provide an answer to the open problem raised by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. This work associates a physical quantity named strong nonlocality with a mathematical quantity called graph connectivity.

中文翻译：

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基于图连通性的具有真正纠缠的强量子非局域性

基于局部可区分性的强非局域性是最近在多方量子系统中引入的一种更强的量子非局域性形式：如果子系统的每个二分都是局部不可约的，则称多方量子态的正交集具有强非局域性。大多数已知结果仅限于具有产品状态的集合。石等人。提出了具有纠缠的强非局部集的第一个结果 [ Phys. 修订版 A 102, 042202 (2020)]，他们质疑具有真正纠缠的强非局部集的存在。在这项工作中，我们将一些特殊的真正纠缠集的强非局域性与一些图的连通性联系起来。使用这种关系，我们成功地构建了具有强非局域性的真正纠缠状态集。因此，我们的构造对 Shi等人给出了否定的答案。的问题，并为 Halder等人提出的开放问题提供了答案。[物理。牧师莱特。 122 , 040403 (2019)]。这项工作将称为强非局域性的物理量与称为图连通性的数学量相关联。