Tighter monogamy relations in multiqubit systems

Abstract

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C, the entanglement of formation E, negativity Nc and Tsallis-q entanglement Tq. Monogamy relations for the αth power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.

Complementary quantum correlations among multipartite systems

“…Theorem 2 gives a general monogamy inequality satisfied by the αth power of quantum correlation for the case of 0 < α < γ and γ ≥ 1. Specifically, using the concurrence as an example, we obtain the monogamy inequality satisfied by αth power of concurrence C α for the case of 0 < α < 2, which was absent in [5]. Furthermore, inequality (16) in Corollary 2 reduces to the monogamy inequality (8) if k = 1 and α = γ ≥ 2, and to the main result in [25] for k = 1.…”

“…Our general monogamy relations can be used to any quantum correlation measures like concurrence, negativity, entanglement of formation, and give rise to tighter monogamy relations than the existing ones in [25] for some classes of quantum states. These monogamy relations can be also used to Tsallis-q entanglement and Renyi-q entanglement, which give new monogamy relations including the existing ones given in [5,12,37] as special cases.…”

Tighter generalized monogamy and polygamy relations for multiqubit systems

“…From Fig. 2 we can see that the difference between the left and right of the generalized monogamy inequality (11) is smaller than that of the result from [21]. Different from the usual monogamy inequalities under the partition A and B 1 ...B N −2 [38], Theorem 2 and Theorem 3 give monogamy relations under the partition AB and C 1 ...C N −2 , which present finer weighted characterizations of the entanglement distributions among the subsystems, as illustrated in Example 2.…”

“…we get J A = J B = . Set y 1 = C α (|W AB|C1C2 ) − (C 2 (ρ AB ) + C 2 (ρ AC1 ) + C 2 (ρ AC2 ))α J A to be the difference between the left and right side of(11). We have…”

Tighter constraints of multiqubit entanglement for negativity

“…Recently, based on the αth power of entanglement measures, many generalized classes of monogamy inequalities were proposed [21][22][23][24][25]. In Ref.…”