Study of nonclassicality in tripartite correlations beyond standard Bell nonlocality paradigm

In the nonsignaling framework, nonclassicality in correlation arising from two spatially separated input-output devices gets manifested, solely, through its \emph{nonlocal} behavior. Study of correlations based on this said feature is commonly known as local-nonlocal paradigm. While in two-party scenario correlations can be of only two types either local or nonlocal, the situation gets more involved for multi-party scenario, \emph{e.g.,} for tripartite scenario, correlations can be of three types: fully local, two-way local, and genuinely nonlocal. Nonsignaling correlations having quantum realization are termed physical. Fully local and certain quantum realizable two-way local tripartite correlations always have a quantum realization with tripartite biseparable states if there is no restriction on the local Hilbert-space dimensions. In this work, we study the quantum simulation of fully local and two-way local tripartite correlations with restricted local Hilbert-space dimensions, in particular we consider $\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2$ quantum systems. Interestingly, in this restricted simulation scenario we find that simulation of certain fully local and two-way local correlations necessarily requires \emph{genuine quantumness} in the three qubit states. This, going beyond the standard nonlocality paradigm, captures a new notion of genuine nonclassicality even in the fully local and two-way local correlations. To explore this newly introduced notion of genuine nonclassicality, we propose two quantities of interest, called \emph{Svetlichny strength} and \emph{Mermin strength}, and extensively study their properties.