Local Equivalence of Multipartite Entanglement

doi:10.1109/JSAC.2020.2969004

	Local Equivalence of Multipartite Entanglement
	Qiao, Youming 1; Sun, Xiaoming 2; Yu, Nengkun 1
	2020-03-01
发表期刊	IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
ISSN	0733-8716
卷号	38 期号:3 页码:568-574
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.
关键词	Quantum entanglement
DOI	10.1109/JSAC.2020.2969004
收录类别	SCI
语种	英语
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
WOS类目	Engineering, Electrical & Electronic ; Telecommunications
WOS记录号	WOS:000523736000015
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/14080
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.