Tighter constraints of multiqubit entanglement for negativity

Abstract

We provide a characterization of multiqubit entanglement monogamy and polygamy constraints in terms of negativity. Using the square of convex-roof extended negativity (SCREN) and the Hamming weight of the binary vector related to the distribution of subsystems proposed in Kim (Phys Rev A 97: 012334, 2018), we provide a new class of monogamy inequalities of multiqubit entanglement based on the αth power of SCREN for α ≥ 1 and polygamy inequalities for 0 ≤ α ≤ 1 in terms of squared convex-roof extended negativity of assistance (SCRENoA). For the case α < 0, we give the corresponding polygamy and monogamy relations for SCREN and SCRENoA, respectively. We also show that these new inequalities give rise to tighter constraints than the existing ones.

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.…”

“…Jin et al [30] presented tighter monogamy relations based on a variety of measures in multiqubit quantum systems. Further some scholars have established a class of monogamy relations in term of Hamming weights [31][32][33][34][35][36][37]. Recently, Gao et al constructed some inequalities and got a class of tighter monogamy relations [38,39].…”

Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

“…the first equality is due to equality (3), the first and second inequality are due to (32) and inequality (12) of Lemma 2 respectively. The first three minima are taken over all possible pure state decompositions of the mixed state ρ…”

“…The authors in [9] proposed the tighter monogamy relations of the αth (0 ≤ α ≤ 2) power of concurrence under different partition. Some tighter monogamy inequalities [10,11,12] were obtained for multipartite entangled systems in entanglement distributions.…”

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

“…with µ ∈ (0, 1]. Next, we provide a class of monogamy and polygamy inequalities which are tighter than inequalities (12), ( 13) and ( 14), respectively, by using the following lemma [45].…”