Verifying hierarchical network nonlocality in general quantum networks  

作　　者：杨舒媛 侯晋川 贺衎 Shu-Yuan Yang;Jin-Chuan Hou;Kan He(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China

出　　处：《Chinese Physics B》2024年第7期199-208,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.12271394 and 12071336);the Key Research and Development Program of Shanxi Province(Grant No.202102010101004)。

摘　　要：Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full network nonlocality(FNN), l-level quantum network nonlocality(l-QNN) was defined in arxiv. 2306.15717 quant-ph(2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.

关 键 词：full network nonlocality hierarchical network nonlocality tree network 

分 类 号：O413[理学—理论物理]