The stabilizer for n-qubit symmetric states

doi:10.1088/1674-1056/27/10/100311

CSpace

	The stabilizer for n-qubit symmetric states
	Shi, Xian 1,2,3
	2018-10-01
发表期刊	CHINESE PHYSICS B
ISSN	1674-1056
卷号	27 期号:10 页码:8
摘要	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.
关键词	symmetric states stabilizer group
DOI	10.1088/1674-1056/27/10/100311
语种	英语
资助项目	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研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000448161800001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31405
专题	中国科学院数学与系统科学研究院
通讯作者	Shi, Xian
作者单位	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
推荐引用方式 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.