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International Journal of Theoretical Physics

Quantum Correlations Through Spin Coherent States

Mostafa Mansour, Zakaria Dahbi, M. Essakhi, Ahmed Salah

Published May 28, 2021• 26 citations
Publisher
DOI
10.1007/s10773-021-04831-y

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Abstract In this paper, we investigate quantum correlations in a qutrit-like superposition of spin coherent states. In particular, the quantum entanglement, the lower bound of the geometric measure of quantum discord, and the lower bound of local quantum uncertainty for the superposition of spin coherent states are examined, and their properties are characterized and compared. The specific dependence of these different correlation quantities on the spin of the system, the coefficient parameters, and the involved coherence parameters is found. As a part of this analysis, conditions for enhanced quantum correlations of qutrit-like superposition states have been identified, which exposes the characteristics of the states based on which the quantum correlations can be controlled and improved.
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.
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.