A comprehensive proof of the Greenberger-Horne-Zeilinger theorem for the four-qubit system
文献类型：期刊论文
| 作者 | Tang, Li; Chen, Zeqian; Zhong, Jie; Ren, Yaofeng; Zhan, Mingsheng |
| 刊名 | ACTA MATHEMATICA SCIENTIA
 |
| 出版日期 | 2007-10-01 |
| 卷号 | 27期号:4页码:753-776 |
| 关键词 | GHZ theorem GHZ state multi-qubit system |
| 英文摘要 | Greenberger-Horne-Zeilinger (GHZ) theorem asserts that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein, Podolsky, and Rosen (EPR). It is known that for a three-qubit system, there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation, which is exactly Mermin's version of the GHZ theorem. This article for a four-qubit system, which was originally studied by GHZ, the authors show that there are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained using certain geometric invariants to characterize the sets of mutually commuting nonlocal spin observables on the four-qubit system. It is proved that there are at most nine elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the four-qubit system, and each GHZ-Mermin-like argument involves a set of at least five mutually commuting four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in GHZ's theorem. Therefore, we present a complete construction of the GHZ theorem for the four-qubit system. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Mathematics |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | BELLS THEOREM ; STATES |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000250770600007 |
| 公开日期 | 2015-08-18 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/4900]  |
| 专题 | 武汉物理与数学研究所_2011年以前论文发表（包括2011年） |
| 作者单位 | 1.Chinese Acad Sci, Wuhan Inst Phys & Math, State Key Lab Magnet Resonance & Atom & Mol Phys, Wuhan 430071, Peoples R China 2.Chinese Acad Sci, Ctr Cold Atom Phys, Wuhan 430071, Peoples R China 3.Chinese Acad Sci, Grad Sch, Wuhan 430071, Peoples R China 4.Naval Univ Engn, Dept Math, Wuhan 430033, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tang, Li,Chen, Zeqian,Zhong, Jie,et al. A comprehensive proof of the Greenberger-Horne-Zeilinger theorem for the four-qubit system[J]. ACTA MATHEMATICA SCIENTIA,2007,27(4):753-776. |
| APA | Tang, Li,Chen, Zeqian,Zhong, Jie,Ren, Yaofeng,&Zhan, Mingsheng.(2007).A comprehensive proof of the Greenberger-Horne-Zeilinger theorem for the four-qubit system.ACTA MATHEMATICA SCIENTIA,27(4),753-776. |
| MLA | Tang, Li,et al."A comprehensive proof of the Greenberger-Horne-Zeilinger theorem for the four-qubit system".ACTA MATHEMATICA SCIENTIA 27.4(2007):753-776. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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