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arXiv:1411.4721

Strong monogamy of quantum entanglement for multi-qubit W-class states

Jeong San Kim

Published Nov 18, 2014• 3 citations
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Abstract

We provide a strong evidence for strong monogamy inequality of multi-qubit entanglement recently proposed in [B. Regula {\em et al.}, Phys. Rev. Lett. {\bf 113}, 110501 (2014)]. We consider a large class of multi-qubit generalized W-class states, and analytically show that the strong monogamy inequality of multi-qubit entanglement is saturated by this class of states.

DOI
10.48550/arxiv.1411.4721

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We provide a strong evidence for strong monogamy inequality of multi-qubit entanglement recently proposed in [B. Regula {\em et al.}, Phys. Rev. Lett. {\bf 113}, 110501 (2014)]. We consider a large class of multi-qubit generalized W-class states, and analytically show that the strong monogamy inequality of multi-qubit entanglement is saturated by this class of states.
We provide strong evidence for the strong monogamy inequality of multiqubit entanglement recently proposed [B. Regula et al., Phys. Rev. Lett. 113, 110501 (2014)]. We consider a large class of multiqubit generalized WWW-class states and analytically show that the strong monogamy inequality of multiqubit entanglement is saturated by this class of states.
We establish two new inequalities, the weighted strong monogamy (WSM) and the maximum residual strong monogamy (MRSM), which sharpen the generalized Coffman-Kundu-Wootters inequity for multiqubit states. The WSM inequality distinguishes itself from the strong monogamy (SM) conjecture [Phys. Rev. Lett. 113, 110501 (2014)] by using coefficients rather than exponents to modulate the weight allocated to various m-partite contributions. In contrast, the MRSM inequality is formulated using only the maximum m-partite entanglement. We find that the residual entanglement of the MRSM inequality can effectively distinguish the separable states. We also compare the tightness of various SM inequalities and provide examples using a four-qubit mixed state and a five-qubit pure state to illustrate the MRSM inequality. These examples characterize the trade-off relations among entanglement components involving varying numbers of qubits. Our results provide a rigorous framework to characterize and quantify the monogamy of multipartite entanglement.
Monogamy is a defining feature of entanglement, having far-reaching applications. Recently, Regula et al. [Phys. Rev. Lett. 113, 110501 (2014)] proposed a stronger version of monogamy relation for concurrence. We have extended the strong monogamy inequality for another entanglement measure, viz., negativity. In particular, we have concentrated on the four-qubit system and provided a detailed study on the status of strong monogamy on pure states. Further, we have analytically provided some classes of states for which negativity and squared negativity satisfy strong monogamy. Numerical evidences have also been shown in proper places. Our analysis also provides cases where strong monogamy is violated.