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arXiv:1604.03419 · Physical Review A

Strong monogamy inequalities for four qubits

Bartosz Regula, Andreas Osterloh, Gerardo Adesso

Published May 31, 2016• 32 citations
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Abstract

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.

DOI
10.1103/physreva.93.052338

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The monogamy inequality in terms of the concurrence, called the Coffman-Kundu-Wootters inequality [V. Coffman et al., Phys. Rev. A 61, 052306 (2000)], and its generalization [T. J. Osborne and F. Verstraete, Phys. Rev. Lett. 96, 220503 (2006)] hold on general nnn-qubit states including mixed ones. In this Brief Report, we consider the monogamy inequalities in terms of the fully entangled fraction and the teleportation fidelity. We show that the monogamy inequalities do not hold on general mixed states, while the inequalities hold on nnn-qubit pure states.