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

Abstract

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.

22+9 pages, 2 figures, accepted for publication in Journal of Physics A: Mathematical and Theoretical

References in corpus (9)

• Necessary and sufficient condition for non-zero quantum discord
• No-local-broadcasting theorem for quantum correlations
• Extremal correlations of the tripartite no-signaling polytope
• Bound non-locality and activation
• Complementarity between entanglement-assisted and quantum distributed random access code
• Tripartite entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios
• Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states
• Nonclassicality of local bipartite correlations
• Operational characterization of quantumness of unsteerable bipartite states

Cited by in corpus (8)

• Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers
• Tripartite entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios
• Distillation of genuine tripartite Einstein-Podolsky-Rosen steering
• Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
• Asymmetric One-Sided Semi-Device-Independent Steerability of Quantum Discordant States
• Characterization of the quantumness of unsteerable tripartite correlations
• Leggett-Garg inequalities for multitime processes
• Contextuality, superlocality and nonclassicality of supernoncontextuality