Influence of joint measurement bases on sharing network nonlocality

Sharing network nonlocality in an extended quantum network scenario is the new paradigm in the development of quantum theory. Here, we investigate the role of elegant joint measurement (usually referred, EJM) bases within an extended bilocal framework for sharing network nonlocality through sequential measurement protocols. The work is essentially based on the newly introduced (Tavakoli in Phys Rev Lett 126:220401, 2021) bilocal inequality with ternary inputs for end parties and EJM as joint measurement bases in \(\hbox {Alice}_n-{Bob}-{Charlie}_m\) scenario. Here, we are able to capture all simultaneous violations of this inequality for \((n,m)\in \{(2,1),(1,2),(1,1),(2,2)\}\) cases. We also observe the criteria for sharing network nonlocality where we find the dependence of the sharing on the amount of entanglement of the joint bases. Furthermore, we capture the implications of nonlinear inequality structures, revealing both symmetrical and asymmetrical violation patterns within this extended configuration. This investigation advances towards both the theoretical formalism and experimental implementation to characterize quantum correlation in complex network structures, thereby it will contribute to the foundational understanding of distributed quantum resources with their information-theoretic constraints.