KMS Of Academy of mathematics and systems sciences, CAS
The stabilizer for n-qubit symmetric states | |
Shi, Xian1,2,3 | |
2018-10-01 | |
Source Publication | CHINESE PHYSICS B |
ISSN | 1674-1056 |
Volume | 27Issue:10Pages:8 |
Abstract | The stabilizer group for an n-qubit state vertical bar phi > is the set of all invertible local operators (ILO) g = g(1 )circle times g(2) circle times ... g(n), g(i) is an element of L (2,C) such that vertical bar phi > = g vertical bar phi >. Recently, Gour et al. [Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58 092204] presented that almost all n-qubit states vertical bar psi > own a trivial stabilizer group when n >= 5. In this article, we consider the case when the stabilizer group of an n-qubit symmetric pure state vertical bar psi > is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state vertical bar phi > is nontrivial when n <= 4. Then we present a class of n-qubit symmetric states vertical bar phi > with a trivial stabilizer group when n >= 5. Finally, we propose a conjecture and prove that an n-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5 under the conjecture we make, which confirms the main result of Gour et al. partly. |
Keyword | symmetric states stabilizer group |
DOI | 10.1088/1674-1056/27/10/100311 |
Language | 英语 |
Funding Project | National Key Research and Development Program of China[2016YFB1000902] ; National Natural Science Foundation of China[61232015] ; National Natural Science Foundation of China[61621003] ; Knowledge Innovation Program of the Chinese Academy of Sciences (CAS) ; Institute of Computing Technology of CAS |
WOS Research Area | Physics |
WOS Subject | Physics, Multidisciplinary |
WOS ID | WOS:000448161800001 |
Publisher | IOP PUBLISHING LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31405 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Shi, Xian |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, UTS AMSS Joint Res Lab Quantum Computat & Quantum, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Shi, Xian. The stabilizer for n-qubit symmetric states[J]. CHINESE PHYSICS B,2018,27(10):8. |
APA | Shi, Xian.(2018).The stabilizer for n-qubit symmetric states.CHINESE PHYSICS B,27(10),8. |
MLA | Shi, Xian."The stabilizer for n-qubit symmetric states".CHINESE PHYSICS B 27.10(2018):8. |
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