Tighter Constraints of Multiqubit Entanglement*

Abstract

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.the squared convex-roof extended negativity (CREN) N 2 c [12, 13] satisfy the monogamy relations for multiqubit states.

Tighter Monogamy and Polygamy Relations of Quantum Entanglement in Multi-qubit Systems

“…But when l = 1 k = 2 and 1<μ ≤ 2, the lower bound ( 19) is better than (18). It can be seen that our result is better than the result (18) in [27] for α ≥ 2, hence better than (17) given in [25], see Fig. 1.…”

“…For given l, the bigger the μ is, the tighter the inequality in Theorem 2.3 is. Therefore, our new monogamy relation for concurrence is better than the ones in [25,27].…”

“…Fig. 1 From top to bottom, the first curve represents the concurrence of |φ A|BC in Example 2.6, the third and fourth curves represent the lower bounds from [27] and [25], respectively. The second curve represents the lower bound from our result…”

“…Some monogamy and polygamy inequalities related to the αth power of entanglement measures have been also proposed. In [24][25][26][27], it is proved that the αth power of concurrence and CREN satisfy the monogamy inequalities in multiqubit systems for α ≥ 2. It has also been shown that the αth power of EoF satisfies monogamy relations when α ≥ √ 2.…”

“…It has also been shown that the αth power of EoF satisfies monogamy relations when α ≥ √ 2. Besides, the αth power of Tsallis-q entanglement and Rényi-α entanglement satisfy monogamy relations when α ≥ 1 for some cases [17,[24][25][26][27]29]. The corresponding polygamy relations have also been established [19-21, 23, 30, 31].…”