Hierarchy of genuine multipartite quantum correlations
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Hierarchy of genuine multipartite quantum correlations Zhih-Ahn Jia1,2 · Rui Zhai3 · Shang Yu1,2 · Yu-Chun Wu1,2 · Guang-Can Guo1,2 Received: 7 May 2020 / Accepted: 29 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Classifying quantum states which exhibit 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 (GMC) for both conceptual and technical difficulties. In this work, we show that, for any N -partite qudit states, there also exists such a hierarchy: genuine multipartite total correlations (GMT) ⊇ genuine multipartite discord (GMD) ⊇ genuine multipartite entanglement (GME) ⊇ genuine multipartite steering (GMS) ⊇ genuine multipartite nonlocality (GMNL). Furthermore, by constructing explicit states, we show that GMT, GME and GMS are inequivalent with each other and thus GMT GME GMS. Keywords Quantum correlation · Quantum entanglement · Quantum steering
1 Introduction Investigating the nature of different kinds of quantum correlations is one of the central problems in quantum information theory [1,2] and quantum many-body physics [3,4]; besides its theoretical interest, it also has a crucial applicative importance. Entangle-
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Zhih-Ahn Jia [email protected] Yu-Chun Wu [email protected]
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CAS Key Laboratory of Quantum Information, School of Physical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
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CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
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Department of Engineering Physics, Institute of Technical Physics, Tsinghua University, Beijing 10084, People’s Republic of China 0123456789().: V,-vol
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ment [5–7] and Bell nonlocality [8] are two prototypical examples, which are among the most striking features of quantum mechanics and they are also important resources for information tasks. The landmark works of Einstein et al. [9] and Bell [10] indicate that quantum theory is beyond the local hidden variable (LHV) model, and the phenomenon has been designated as nonlocality. Since then, many new kinds of quantum correlations have been extensively investigated, for example total correlation and quantum discord [11–15] which is the measure of nonclassical correlations between two subsystems of a physical system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement [11–15]. The other one is quantum steering [16] which is initially introduced by Schrödinger [17] and recently rigorously defined by Wiseman et al. [18] to describe the ability of one experimente
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