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In the literature on $K$-locality ($K\geq2$) networks, the local hiddenvariables are strictly distributed in the specific observers rather than thewhole ones. Regarding genuine Bell locality, all local hidden variables, asclassical objects that allow for perfect cloning in classical physics, shouldbe cloned and then spread throughout the networks. More correlators areinvolved in the proposed linear and non-linear Bell-type inequalities, wheretheir upper bounds are specified by the pre-determined output probabilitydistribution. As for the quantum version, the no-clone theorem limits thebroadcast of quantum correlations. To explore genuine Bell nonlocality invariant particle distributions in the networks, the Pauli operators stabilizingthe two-qubit Bell states or multi-qubit Greenberger--Horne--Zeilinger states(GHZ states) play an essential role in designing the proposed linear andnon-linear Bell tests and assigning the local incompatible measurements for thespatially separated observers. We prove the maximal violations of the proposedBell-type inequalities quantum networks. In the end, how entanglement swappingreplaces the joint measurements in the Bell tests is demonstrated.

Genuine Bell locality and nonlocality in the networks