Polygamy relations for tripartite and multipartite quantum systems

We study the polygamy property in tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a sufficient and necessary condition of the set for continuous measure of quantum correlation Q to be polygamous. In multipartite system, we provide generalized definitions for polygamy in n-qubit systems with n >= 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 4$$\end{document}, and then, we build polygamy inequalities with a polygamy power beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}. Next we also describe that any entanglement of assistance can be polygamy according to our new definition in multipartite systems. For better understanding, we use right triangle and tetrahedron to explain our new polygamy relations. Moreover, the polygamy relations between each single qubit and its remaining partners are also investigated to enrich our results.