Entanglement of formation and quantum discord in multipartite j-spin coherent states.

Hicham Baba, Mostafa Mansour, Mohammed Daoud A

Steve Campbell

H. Baba, W. Kaydi, Mohammed Daoud A +1 more

We study the entanglement of formation and the quantum discord contained in even and odd multipartite [Formula: see text]-spin coherent states. The key element of this investigation is the fact that a single [Formula: see text]-spin coherent state is viewed as comprising [Formula: see text] qubit states. We compute the quantum correlations present in the n even and odd [Formula: see text]-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the different qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite [Formula: see text]-spin coherent states.

L.S. Lima

Mohammed Daoud A, R. Ahl Laamara, W. Kaydi

The key ingredient of the approach presented in this paper is the factorization property of SU (2) coherent states upon the splitting or decay of a quantum spin system. In this picture, the even and odd spin coherent states are viewed as comprising two, three or more spin sub-systems. From this perspective, we investigate the multipartite quantum correlations defined as the sum of the correlations of all possible bi-partitions. The pairwise quantum correlations are quantified by entanglement of formation and quantum discord. Special attention is devoted to tripartite splitting schemes. We explicitly derive the sum of the entanglement of formation for all possible bi-partitions. It coincides with the sum of all possible occurrences of pairwise quantum discord. The conservation relation between the distribution of entanglement of formation and quantum discord in the tripartite splitting scheme is discussed. We show that entanglement of formation and quantum discord possess the monogamy property for even spin coherent states, in contrast to odd ones which violate the monogamy relation when the overlap of the coherent states approaches unity.

Zhihao Ma, ZhiHua Chen, F. F. Fanchini

In this paper, we present a measure of quantum correlation for a multipartite system, defined as the sum of the correlations for all possible partitions. Our measure can be defined for quantum discord (QD), geometric quantum discord or even for entanglement of formation (EOF). For tripartite pure states, we show that the multipartite measures for the QD and the EOF are equivalent, which allows direct comparison of the distribution and the robustness of these correlations in open quantum systems. We study dissipative dynamics for two distinct families of entanglement: a W state and a GHZ state. We show that, for the W state, the QD is more robust than the entanglement, while for the GHZ state, this is not true. It turns out that the initial genuine multipartite entanglement present in the GHZ state makes the EOF more robust than the QD.