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arXiv · 1711.04664

Hierarchy of Genuine Multipartite Quantum Correlations

Zhih-Ahn Jia·Rui Zhai·Shang Yu·Yu-Chun Wu·Guang-Can Guo
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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) $\supsetneq$ discord (D) $\supsetneq$ entanglement (E) $\supsetneq$ steering (S) $\supsetneq$ 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 $\supsetneq$ GME $\supsetneq$ GMS.

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Zhih-Ahn Jia, Rui Zhai, Shang Yu, Yu-Chun Wu, Guang-Can Guo. 2017-11-13. Hierarchy of Genuine Multipartite Quantum Correlations. https://doi.org/10.1007/s11128-020-02922-z

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