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Pure state 'really' informationally complete with rank-1 POVM
Wang, Yu1,2; Shang, Yun1,3,4
AbstractWhat 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.
KeywordQuantum state tomography Pure state Quantum measurement Rank-1 operators
Funding ProjectNational 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 Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000426380900006
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Document Type期刊论文
Affiliation1.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
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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.
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