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Polygamy relations of multipartite systems

Jin, Z., Fei, S., Qiao, C.

Published Jan 1, 2019• 5 citations
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Abstract

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $$\alpha $$ th $$(\alpha \ge 2)$$ power of concurrence of assistance, $$\beta $$ th $$(\beta \ge 1)$$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).

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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).
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.
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 study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the α\alphaαth (α≥2\alpha\geq 2α≥2) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the β\betaβth (0≤β≤20\leq \beta\leq20≤β≤2) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-qqq entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.
Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th (0 ≤ γ ≤ α, α ≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-th (δ ≥ β, 0 ≤ β ≤ 1) power of entanglement of assistance based on unified-(q,s) entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of γ and δ. These results are then applied to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.
Abstract This study provides a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, it presents polygamy inequalities satisfied by the βth power of the quantum correlation measures. Taking concurrence of assistance as an example, it further illustrates the significance and advantages of these relations. It also obtains a polygamy relation with equality by considering the one‐to‐group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. It demonstrates that such relations for tripartite states can be generalized to multipartite systems.