Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario

For a bipartite local quantum correlation, superlocality refers to the requirement for a larger dimension of the random variable in the classical simulation protocol than that of the quantum states that generate the correlations. In this work, we consider the classical simulation of local tripartite quantum correlations $P$ among three parties $A, B$ and $C$. If at least one of the bipartitions $(A|BC)$, $(B|AC)$ and $(C|AB)$ is superlocal, then $P$ is said to be absolutely superlocal, whereas if all three bipartitions are superlocal, then $P$ is said to be genuinely superlocal. We present specific examples of genuine superlocality for tripartite correlations derived from three-qubit states. It is argued that genuine quantumness as captured by the notion of genuine discord is necessary for demonstrating genuine superlocality. Finally, the notions of absolute and genuine superlocality are also defined for multipartite correlations.