Verifying hierarchical network nonlocality in general quantum networks

doi:10.1088/1674-1056/ad3dd5

Abstract 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.

Keywords: full network nonlocality hierarchical network nonlocality tree network

Received: 26 February 2024
Revised: 31 March 2024
Accepted manuscript online: 12 April 2024

PACS:	03.67.Hk	(Quantum communication)
	03.67.-a	(Quantum information)
	03.65.-w	(Quantum mechanics)
	03.65.Aa	(Quantum systems with finite Hilbert space)

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

Corresponding Authors: Kan He
E-mail: hekanquantum@163.com

Cite this article:

Shu-Yuan Yang(杨舒媛), Jin-Chuan Hou(侯晋川), and Kan He(贺衎) Verifying hierarchical network nonlocality in general quantum networks 2024 Chin. Phys. B 33 070304

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Verifying hierarchical network nonlocality in general quantum networks

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