Study of nonclassicality in tripartite correlations beyond standard Bell nonlocality paradigm

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.

12 pages, 1 figure, Accepted for publication in Quantum Studies: Mathematics and Foundations

References in corpus (11)

• Necessary and sufficient condition for non-zero quantum discord
• No-local-broadcasting theorem for quantum correlations
• Operational interpretations of quantum discord
• Extremal correlations of the tripartite no-signaling polytope
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Bound non-locality and activation
• Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states
• Detecting genuine multipartite entanglement in steering scenarios
• Efficient Test to Demonstrate Genuine Three Particle Nonlocality
• Characterizing quantum correlations in the nonsignaling framework
• Canonical decomposition of quantum correlations in the framework of generalized nonsignaling theories

Cited by in corpus (6)

• Nonclassicality of local bipartite correlations
• Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
• Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario
• Local marginals ameliorate device independent witnessing of genuine entanglement
• Characterizing quantum correlations in the nonsignaling framework
• Characterization of the quantumness of unsteerable tripartite correlations