Tighter monogamy and polygamy relations for a superposition of the generalized W-class state and vacuum

Abstract

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized W-class state and vacuum in terms of the Tsallis-q entanglement and the Rényi-α entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.

Monogamy of quantum entanglement

“…, n. In Ref. [57][58][59][60][61][62][63], polygamy inequalities were also established for other entanglement measures.…”

“…On the other hand, the polygamous property can be regarded as another kind of entanglement constraints in multiqubit systems, and Gour et al [54] established the first dual polygamy inequality for multi-qubit systems using concurrence of Assistance(CoA). Subsequently, polygamy inequalities was generalized into various entanglement measures [55][56][57][58][59][60][61][62][63][64].…”

Monogamy of Quantum Entanglement

“…., n. In Refs. [57][58][59][60][61][62][63], polygamy inequalities were also established for other entanglement measures.…”

“…Recently, Shi et al presented in [47] new monogamy and polygamy relations for n-qudit generalized W-class states and vacuum (GWV) states in terms of the TqE. In [59,92] the authors investigated the monogamy and polygamy relations for the GWV states in highdimensional systems in terms of the RαE. Except for squashed entanglement and one-way distillable entanglement, monogamy relations for various entanglement measures only hold for some special high-dimensional states.…”

“…On the other hand, the polygamous property can be regarded as another kind of entanglement constraints in multi-qubit systems, and Gour et al [54] established the first dual polygamy inequality for multi-qubit systems using concurrence of Assistance (CoA). Subsequently, polygamy inequalities was generalized into various entanglement measures [55][56][57][58][59][60][61][62][63][64].…”