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

Abstract

We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and Rényi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and Rényi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented.

Tighter monogamy relations in multiparty quantum systems

“…Then, by making full use of the new inequality, we establish a general framework of monogamy relations for arbitrary quantum states. The lower bounds obtained by us are tighter than existing ones [30][31][32][33][34][35][36][37][39][40][41][42]. To illustrate our results obviously, two examples are presented in term of the µ-th power of concurrence.…”

“…The red line represents the lower bound from the result in [39] with k = 2. The yellow line represents the lower bound from the result in [40] with k = 2. The purple line represents the lower bound from the result in [34][35][36][37] with k = 2.…”

General monogamy and polygamy properties of quantum systems

“…This polygamy relation has been generalized to multipartite systems for various assisted entanglement measures such as the squared concurrence of assistance C 2 a [28], entanglement of assistance E a [17,29], the βth (0 ≤ β ≤ 2) power of convex-roof extended negativity of assistance N β a [30]. Similar to the monogamy relation, the corresponding tighter polygamy relations have also been established for different kinds of assisted entanglements [22,25,26].…”

“…According to the CKW inequality, the monogamy relation was generalized to other entanglement measure such as convex-roof extended negativity N [18][19][20]. Moreover, it has been shown that these entanglement measures to the αth power do satisfies tighter monogamy relations of tripartite systems and multipartite systems [23][24][25][26].…”

“…However, the relations in Ref. [26] with different parameter ranges is unknown. In this paper, based on the previous results, we obtain general monogamy inequalities of any entanglement measure satisfying E γ A|BC ≥ E γ AB +E γ AC , so that the entanglement distribution can be described more accurately for quantum states that satisfy the stronger constraints.…”