Pure state 'really' informationally complete with rank-1 POVM

doi:10.1007/s11128-018-1812-2

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	Pure state 'really' informationally complete with rank-1 POVM
	Wang, Yu 1,2; Shang, Yun1,3,4
	2018-03-01
发表期刊	QUANTUM INFORMATION PROCESSING
ISSN	1570-0755
卷号	17 期号:3 页码:11
摘要	What is the minimal number of elements in a rank-1 positive operator-valued measure (POVM) which can uniquely determine any pure state in d-dimensional Hilbert space H-d? The known result is that the number is no less than 3d - 2. We show that this lower bound is not tight except for d = 2 or 4. Then we give an upper bound 4d - 3. For d = 2, many rank-1 POVMs with four elements can determine any pure states in H-2. For d = 3, we show eight is the minimal number by construction. For d = 4, the minimal number is in the set of {10, 11, 12, 13}. We show that if this number is greater than 10, an unsettled open problem can be solved that three orthonormal bases cannot distinguish all pure states in H-4. For any dimension d, we construct d + 2k - 2 adaptive rank-1 positive operators for the reconstruction of any unknown pure state in H-d, where 1 <= k <= d.
关键词	Quantum state tomography Pure state Quantum measurement Rank-1 operators
DOI	10.1007/s11128-018-1812-2
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB1000902] ; National Research Foundation of China[61472412] ; Program for Creative Research Group of National Natural Science Foundation of China[61621003]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000426380900006
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29617
专题	数学所
通讯作者	Shang, Yun
作者单位	1.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, AMSS, NCMIS, Beijing 100190, Peoples R China 4.Chinese Acad Sci, MDIS, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Yu,Shang, Yun. Pure state 'really' informationally complete with rank-1 POVM[J]. QUANTUM INFORMATION PROCESSING,2018,17(3):11.
APA	Wang, Yu,&Shang, Yun.(2018).Pure state 'really' informationally complete with rank-1 POVM.QUANTUM INFORMATION PROCESSING,17(3),11.
MLA	Wang, Yu,et al."Pure state 'really' informationally complete with rank-1 POVM".QUANTUM INFORMATION PROCESSING 17.3(2018):11.