Nonlocal sets of orthogonal product states with the less amount of elements in tripartite quantum systems View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

Yan-Ying Zhu, Dong-Huan Jiang, Xiang-Qian Liang, Guang-Bao Xu, Yu-Guang Yang

ABSTRACT

Many achievements have been made since quantum nonlocality without entanglement was found. A natural question is how many orthogonal product states (OPSs) are needed at least to form a nonlocal set in a given quantum system. In this paper, we achieve some interesting results about nonlocal sets with the less amount of OPSs. Firstly, we construct new nonlocal sets of OPSs with only 6 and 9 members in the C3⊗C3⊗C3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^{3} \otimes \mathbb {C}^{3} \otimes \mathbb {C}^{3}$$\end{document} and C4⊗C4⊗C4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^{4} \otimes \mathbb {C}^{4} \otimes \mathbb {C}^{4}$$\end{document} quantum systems, respectively. Secondly, we give a general construction of nonlocal set of OPSs with only 3(d-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3(d-1)$$\end{document} members in Cd⊗Cd⊗Cd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^{d}\otimes \mathbb {C}^{d}\otimes \mathbb {C}^{d}$$\end{document} quantum system for d≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 3$$\end{document}. Finally, we compare our work with existing results and make a series of generalizations. The comparison result shows that the nonlocal sets of OPSs constructed by us have the least number of elements in their corresponding quantum systems. More... »

PAGES

252

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11128-022-03601-x

DOI

http://dx.doi.org/10.1007/s11128-022-03601-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1149785501


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