Tighter constraints of multiqubit entanglement in terms of unified entropy

Abstract

We present classes of monogamy inequalities related to the αth (α ⩾ 1) power of the entanglement measure based on the unified-(q, s) entropy, and polygamy inequalities related to the βth (0 ⩽ β ⩽ 1) power of the unified-(q, s) entanglement of assistance by using Hamming weight. We show that these monogamy and polygamy inequalities are tighter than the existing ones. Detailed examples are given for illustrating the advantages.

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 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.…”

“…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].…”

On monogamy and polygamy relations of multipartite systems

“…where  is a bipartite entanglement measure, A A r . The monogamy relation was generalized to multiqubit quantum systems, high-dimensional quantum systems in general settings [3][4][5][6][7][8][9][10][11][12][13]. The first polygamy relation of entanglement was established in [14] for some threequbit system as the inequality…”