Network nonlocality sharing in a two-forked tree-shaped network
Hao Sun, Fen-Zhuo Guo, Haifeng Dong, Fei Gao · Physical Review A · 2024
Quantum network nonlocality sharing provides a unique perspective for constructing large-scale quantum networks and holds promise for numerous potential applications. In this paper we demonstrate the network nonlocality sharing via unsharp measurements in a two-forked $n$-layer tree-shaped network, which features ${2}^{n}\ensuremath{-}2$ independent sources and ${2}^{n}\ensuremath{-}1$ nodes. We investigate the $({2}^{n}\ensuremath{-}2)$-local scenarios via any $m$-sided sequential measurements, and conclude that arbitrarily many independent observers on each sequential side can share the non-$({2}^{n}\ensuremath{-}2)$-locality for a sufficiently large value of $n$. For a finite $n$, we present a method that enables directly obtaining the number of observers on each sequential side, who can share the non-$({2}^{n}\ensuremath{-}2)$-locality simultaneously. To interpret our results more intuitively, we discuss the simplest case of $n=3$, and find that at most 30, 6, 3, and 2 sequential observers per sequential side can simultaneously share the non-6-locality in $m$-sided cases for $m=1,2,3,4$, respectively.