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The stabilizer for n-qubit symmetric states
Shi, Xian1,2,3
2018-10-01
Source PublicationCHINESE PHYSICS B
ISSN1674-1056
Volume27Issue:10Pages:8
AbstractThe 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.
Keywordsymmetric states stabilizer group
DOI10.1088/1674-1056/27/10/100311
Language英语
Funding ProjectNational 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 AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000448161800001
PublisherIOP PUBLISHING LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31405
Collection中国科学院数学与系统科学研究院
Affiliation1.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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