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Maximum $N$-body correlations do not in general imply genuine multipartite entanglement

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Christopher Eltschka1 and Jens Siewert2,3

1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
2Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
3IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain

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Abstract

The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong $N$-party correlations with $N$-party entanglement in an $N$-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest $N$-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest $N$-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation.

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Cited by

[1] Daniel Miller, “Small quantum networks in the qudit stabilizer formalism”, arXiv:1910.09551.

[2] Cornelia Spee, “Certifying the purity of quantum states with temporal correlations”, arXiv:1909.06233.

The above citations are from SAO/NASA ADS (last updated successfully 2020-02-10 17:18:22). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2020-02-10 17:18:20: Could not fetch cited-by data for 10.22331/q-2020-02-10-229 from Crossref. This is normal if the DOI was registered recently.

Source: https://quantum-journal.org/papers/q-2020-02-10-229/

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