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Local Equivalence of Multipartite Entanglement

文献类型：期刊论文

作者Qiao, Youming1; Sun, Xiaoming2; Yu, Nengkun1
刊名IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
出版日期2020-03-01
卷号38期号:3页码:568-574
关键词Quantum entanglement
ISSN号0733-8716
DOI10.1109/JSAC.2020.2969004
英文摘要Let R be an invariant polynomial ring of a reductive group acting on a vector space, and let d be the minimum integer such that R is generated by those polynomials in R of degree no more than d. To upper bound such d is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite entanglement, we study the invariant polynomial rings of local unitary groups - the direct product of unitary groups acting on the tensor product of Hilbert spaces, and local general linear groups - the direct product of general linear groups acting on the tensor product of Hilbert spaces. For these two group actions, we prove explicit upper bounds on the degrees needed to generate the corresponding invariant polynomial rings. On the other hand, systematic methods are provided to construct all homogeneous polynomials that are invariant under these two groups for any fixed degree. Thus, our results can be regarded as a complete characterization of the invariant polynomial rings. As an interesting application, we show that multipartite entanglement is additive in the sense that two multipartite states are local unitary equivalent if and only if r-copies of them are local unitary equivalent for some r.
资助项目Singapore Ministry of Education ; National Research Foundation ; Australian Research Council[DE150100720] ; National Natural Science Foundation of China[61832003] ; National Natural Science Foundation of China[61761136014] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB28000000] ; K. C. Wong Education Foundation ; Natural Sciences and Engineering Research Council of Canada (NSERC) ; NSERC Discovery Accelerator Supplements (DAS) ; Canada Research Chairs Program (CRC) ; Canadian Institute for Advanced Research (CIFAR) ; [DE180100156]
WOS研究方向Engineering ; Telecommunications
语种英语
WOS记录号WOS:000523736000015
出版者IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
源URL[http://119.78.100.204/handle/2XEOYT63/14079]  
专题中国科学院计算技术研究所期刊论文_英文
通讯作者Qiao, Youming
作者单位1.Univ Technol Sydney, Sch Software, Fac Engn & Informat Technol, Ctr Quantum Software & Informat, Sydney, NSW 2007, Australia
2.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Qiao, Youming,Sun, Xiaoming,Yu, Nengkun. Local Equivalence of Multipartite Entanglement[J]. IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,2020,38(3):568-574.
APA Qiao, Youming,Sun, Xiaoming,&Yu, Nengkun.(2020).Local Equivalence of Multipartite Entanglement.IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,38(3),568-574.
MLA Qiao, Youming,et al."Local Equivalence of Multipartite Entanglement".IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 38.3(2020):568-574.

入库方式： OAI收割

来源：计算技术研究所

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