Generalized n-locality correlations in tree tensor network configuration

Quantum correlations in various quantum networks are fundamental for quantum communications, among which Bell nonlocality in networks have already been intensively studied. In this paper, Bell nonlocality for the tree tensor network are discussed by considering two general cases: One case is that each party of the network performs arbitrary number of binary measurements, while the other case is that four extreme parties perform arbitrary m(m≥2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m\ge 2)$$\end{document} binary measurements and all intermediate parties perform 2m-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{m-1}$$\end{document} binary measurements. For both cases, different n-locality inequalities are established and the corresponding quantum violations are also examined.