Network nonlocality sharing via weak measurements in the generalized star network configuration

Network nonlocality exhibits completely novel quantum correlations compared to standard quantum nonlocality. It has been shown that network nonlocality can be shared in a generalized bilocal scenario via weak measurements [Phys. Rev. A. 105, 042436 (2022)]. In this paper, we investigate network nonlocality sharing via weak measurements in a generalized star-shaped network configuration with arbitrary numbers of unbiased dichotomic input $k$, which includes $n$ branches and adds ($m$-1) more parties in each branch to the original star network $(n, m=1, k=2)$ scenario. It is shown that network nonlocality sharing among all observers can be revealed from simultaneous violation of $2^n$ inequalities in the ($n, m=2, k=2$) and ($n, m=2, k=3$) scenarios for any $n$ branches. The noise resistance of network nonlocality sharing with a precise noise model is also analyzed.