Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

Weighted monogamy and polygamy relations

“…Our new method puts both monogamy and polygamy relations in the same setting and we show that the equilibrium occurs exactly at the measurement of the multipartite system. Our study gives tighter bounds than some of the recent relations [20][21][22][23]. Especially, we show that the weighted monogamy and polygamy are significantly better than the usual monogamy and polygamy (see detailed examples).…”

“…Naturally, our relations based on lemma 2.1 will outperform those given in [23, lemma 2], and subsequently also [20][21][22]. Now let us first utilize the lemma for the monogamy relation.…”

“…where the middle term corresponds to our lower bound and the last term was that of [23, theorem 2]. Since [23] provided stronger bounds than [20][21][22], any monogamy relations based on lemma 2.1 will produce tighter bounds than those given in [20][21][22] as well.…”

“…Applying the monogamy relations in [20] to quantum correlations like squared convex-roof extended negativity, entanglement of formation, and concurrence one can get tighter monogamy inequalities than those given in [9]. In [21,22], Jin et al gave another set of monogamy relations for (0 ⩽ α ⩽ γ 2 , γ ⩾ 2) and polygamy relations for (β ⩾ δ, 0 ⩽ δ ⩽ 1), the bound is stronger than [20] in the monogamy case but weaker in polygamy case. Recently, Zhang et al [23] rigorously proved that their monogamy and polygamy are tighter than those given in [20][21][22].…”

“…In [21,22], Jin et al gave another set of monogamy relations for (0 ⩽ α ⩽ γ 2 , γ ⩾ 2) and polygamy relations for (β ⩾ δ, 0 ⩽ δ ⩽ 1), the bound is stronger than [20] in the monogamy case but weaker in polygamy case. Recently, Zhang et al [23] rigorously proved that their monogamy and polygamy are tighter than those given in [20][21][22]. In [24][25][26] another type of monogamy relations has also been proposed.…”