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arXiv:1903.11350 · Journal of Physics A Mathematical and Theoretical

Polygamy relations of multipartite entanglement beyond qubits

Zhi-Xiang Jin, Shao-Ming Fei

Published Mar 12, 2019• 5 citations
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Abstract

Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.

DOI
10.1088/1751-8121/ab0ed9

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Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.
We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the α\alphaαth (0≤α≤2)(0\leq \alpha\leq 2)(0≤α≤2) power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the β\betaβth (0≤β≤10\leq \beta \leq 10≤β≤1) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.
We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the α\alpha α th (α≥2)(\alpha \ge 2)(α≥2) power of concurrence of assistance, β\beta β th (β≥1)(\beta \ge 1)(β≥1) power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).
Abstract Based on q -expected entanglement measure for q ⩾ 1 , we generalize the polygamy inequality for multiparty entanglement in arbitrary-dimensional quantum systems. By using the β th-power of the q -expected entanglement of assistance for 0 ⩽ β ⩽ 1 and the Hamming weight of the binary vector related with the distribution of subsystems, a class of weighted polygamy inequalities in arbitrary-dimensional quantum systems is established. We further demonstrate that our class of weighted polygamy inequalities can be improved even into tighter inequalities, under some conditions, with auxiliary entanglement in bipartite subsystems. Our results may provide new ideas for studying the polygamy constraints of multiparty entanglement and better characterizing the entanglement distribution.
We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary-dimensional quantum systems. By using the $\ensuremath{\beta}\mathrm{th}$ power of entanglement of assistance for $0\ensuremath{\le}\ensuremath{\beta}\ensuremath{\le}1$ and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of weighted polygamy inequalities of multiparty entanglement in arbitrary-dimensional quantum systems. We further show that our class of weighted polygamy inequalities can even be improved to be tighter inequalities with some conditions on the assisted entanglement of bipartite subsystems.
The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.