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Monogamy properties of qubit systems

Zhu, X., Fei, S.

Published Jan 1, 2019• 8 citations
OpenAlex

Abstract

We investigate monogamy relations related to quantum entanglement for $n-$qubit quantum systems. General monogamy inequalities are presented to the $\beta$th $(\beta\in(0,2))$ power of concurrence, negativity and the convex-roof extended negativity, as well as the $\beta$th $(\beta\in(0,\sqrt{2}))$ power of entanglement of formation. These monogamy relations are complementary to the existing ones with different regions of parameter $\beta$. In additions, new monogamy relations are also derived which include the existing ones as special cases.

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We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the $\ensuremath{\alpha}\text{th}$ power of concurrence and entanglement of formation are presented for NNN-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
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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.
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