Hierarchy of Genuine Multipartite Quantum Correlations

Abstract

Classifying states which exhibiting different statistical correlations is among the most important problems in quantum information science and quantum many-body physics. In bipartite case, there is a clear hierarchy of states with different correlations: total correlation (T) $⊋$ discord (D) $⊋$ entanglement (E) $⊋$ steering (S) $⊋$ Bell~nonlocality (NL). However, very little is known about genuine multipartite correlations (GM$\mathcal{C}$) for both conceptual and technical difficulties. In this work, we show that, for any $N$-partite qudit states, there also exist such a hierarchy: genuine multipartite total correlations (GMT) $\supseteq$ genuine multipartite discord (GMD) $\supseteq$ genuine multipartite entanglement (GME) $\supseteq$ genuine multipartite steering (GMS) $\supseteq$ genuine multipartite nonlocality (GMNL). Furthermore, by constructing precise states, we show that GMT, GME and GMS are inequivalent with each other, thus GMT $⊋$ GME $⊋$ GMS.

References in corpus (8)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Grothendieck's constant and local models for noisy entangled quantum states
• Noise robustness of the nonlocality of entangled quantum states
• Experimental violation of Svetlichny's inequality
• Local hidden--variable models for entangled quantum states
• Quantifying genuine multipartite correlations and their pattern complexity
• Constructions of genuinely entangled multipartite states with applications to local hidden variables (LHV) and states (LHS) models

Cited by in corpus (7)

• Optimal tests of genuine multipartite nonlocality
• Hexapartite steering based on a four-wave-mixing process with a spatially structured pump
• Entanglement and quantum discord in the cavity QED models
• Generating quantum dissonance via local operations
• EPR steering in symmetrical Gaussian states
• Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states
• Bounds on Multipartite Nonlocality via Reduction to Biased Nonlocality