N-qudit SLOCC equivalent W states are determined by their bipartite reduced density matrices with tree form
N-qudit SLOCC equivalent W states are determined by their bipartite reduced density matrices with tree form
复制标题
N-qudit SLOCC 等效 W 状态由树形二分约化密度矩阵确定
DOI：
10.1007/s11128-020-02918-9
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发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
Fei Gao
中科院分区：
文献类型：
--
作者：
Xia Wu;Hengyue Jia;D;an Li;Fei Gao
It has been proved that N-qudit (i.e., d-level subsystems) generalized W states are determined by their bipartite reduced density matrices. In this paper, we prove that only (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} of the bipartite reduced density matrices are sufficient. Furthermore, we find that N-qudit W states preserve their determinability under stochastic local operation and classical communication (SLOCC). That is, all multipartite pure states that are SLOCC equivalent to N-qudit W states can be uniquely determined (among pure, mixed states) by their (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} of the bipartite reduced density matrices, if the (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} pairs of qudits constitute a tree graph on N vertices, where each pair of qudits represents an edge.
It has been proved that N-qudit (i.e., d-level subsystems) generalized W states are determined by their bipartite reduced density matrices. In this paper, we prove that only (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} of the bipartite reduced density matrices are sufficient. Furthermore, we find that N-qudit W states preserve their determinability under stochastic local operation and classical communication (SLOCC). That is, all multipartite pure states that are SLOCC equivalent to N-qudit W states can be uniquely determined (among pure, mixed states) by their (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} of the bipartite reduced density matrices, if the (N-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(N-1)$$\end{document} pairs of qudits constitute a tree graph on N vertices, where each pair of qudits represents an edge.
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