Study of nonclassicality in tripartite correlations beyond standard Bell nonlocality paradigm

TL;DR

This paper investigates a new form of nonclassicality in tripartite correlations beyond standard Bell nonlocality, showing that certain local correlations require genuine quantumness in three-qubit states under dimension restrictions.

Contribution

It introduces the concepts of Svetlichny strength and Mermin strength to quantify genuine nonclassicality in tripartite correlations beyond traditional nonlocality.

Findings

Certain fully local and two-way local correlations require genuine quantumness in three-qubit states.

Proposed Svetlichny strength and Mermin strength as measures of this nonclassicality.

Dimension restrictions reveal new nonclassical features beyond standard Bell nonlocality.

Abstract

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.