NEW BOUNDS OF MUTUALLY UNBIASED MAXIMALLY ENTANGLED BASES IN Cd circle times C-kd | |
Cheng, Xiaoya1,2; Shang, Yun1,3,4 | |
2018-11-01 | |
Source Publication | QUANTUM INFORMATION & COMPUTATION |
ISSN | 1533-7146 |
Volume | 18Issue:13-14Pages:1152-1164 |
Abstract | Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p(a) - 1) MUMEBs in C-d circle times C-d by properties of Cuss sums for arbitrary odd d. It improves the known lower bound p(a) - 1 for odd d. Certainly, it also generalizes the lower bound 2(p(a) - 1) for d being a single prime power. Furthermore, we construct MUMEBs in C-d circle times C-kd for general k >= 2 and odd d. We get the similar lower bounds as k, b are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in C-d circle times C-kd, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases. |
Keyword | mutually unbiased bases maximally entangled states Pauli matrices mutually orthogonal Latin squares |
Language | 英语 |
Funding Project | National Key Research and Development Program of China[2016YFB1000902] ; National Research Foundation of China[61472412,61872352] ; Program for Creative Research Group of National Natural Science Foundation of China[61621003] |
WOS Research Area | Computer Science ; Physics |
WOS Subject | Computer Science, Theory & Methods ; Physics, Particles & Fields ; Physics, Mathematical |
WOS ID | WOS:000453009400006 |
Publisher | RINTON PRESS, INC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31985 |
Collection | 数学所 |
Corresponding Author | Shang, Yun |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Key Lab Management, Decis & Informat Syst, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Cheng, Xiaoya,Shang, Yun. NEW BOUNDS OF MUTUALLY UNBIASED MAXIMALLY ENTANGLED BASES IN Cd circle times C-kd[J]. QUANTUM INFORMATION & COMPUTATION,2018,18(13-14):1152-1164. |
APA | Cheng, Xiaoya,&Shang, Yun.(2018).NEW BOUNDS OF MUTUALLY UNBIASED MAXIMALLY ENTANGLED BASES IN Cd circle times C-kd.QUANTUM INFORMATION & COMPUTATION,18(13-14),1152-1164. |
MLA | Cheng, Xiaoya,et al."NEW BOUNDS OF MUTUALLY UNBIASED MAXIMALLY ENTANGLED BASES IN Cd circle times C-kd".QUANTUM INFORMATION & COMPUTATION 18.13-14(2018):1152-1164. |
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