From stabilizer states to SIC-POVM fiducial states

doi:10.1134/S004057792212008X

	From stabilizer states to SIC-POVM fiducial states
	Feng, Lingxuan 1,2; Luo, Shunlong 1,2
刊名	THEORETICAL AND MATHEMATICAL PHYSICS
	2022-12-01
卷号	213 期号:3 页码:1747-1761
关键词	stabilizer states SIC-POVMs fiducial states p-norms Zauner's conjecture
ISSN号	0040-5779
DOI	10.1134/S004057792212008X
英文摘要	In the stabilizer formalism of quantum computation, the Gottesman-Knill theorem shows that universal fault-tolerant quantum computation requires the resource called magic (nonstabilizerness). Thus stabilizer states serve as classical states, and states beyond them are necessary for genuine quantum computa-tion. Characterization, detection, and quantification of magic states are basic issues in this context. In the paradigm of quantum measurement, symmetric informationally complete positive operator valued measures (SIC-POVMs, further abbreviated as SICs) play a prominent role due to their structural sym-metry and remarkable features. However, their existence in all dimensions, although strongly supported by extensive theoretical and numerical evidence, remains an elusive open problem (Zauner's conjecture). A standard method for constructing SICs is via the orbit of the Heisenberg-Weyl group on a fiducial state, and most known SICs arise in this way. A natural question arises regarding the relation between stabilizer states and fiducial states. In this paper, we connect them by showing that they are on two extremes with respect to the p-norms of characteristic functions of quantum states. This not only reveals a simple path from stabilizer states to SIC fiducial states, showing quantitatively that they are as far away as possible from each other, but also provides a simple reformulation of Zauner's conjecture in terms of extremals for the p-norms of characteristic functions. A convenient criterion for magic states and some interesting open problems are also presented.
资助项目	National Key R&D Program of China ; National Natural Science Foundation of China[2020YFA0712700] ; [11875317] ; [61833010]
WOS研究方向	Physics
语种	英语
出版者	MAIK NAUKA/INTERPERIODICA/SPRINGER
WOS记录号	WOS:000902029200008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60506]
专题	中国科学院数学与系统科学研究院
通讯作者	Luo, Shunlong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Feng, Lingxuan,Luo, Shunlong. From stabilizer states to SIC-POVM fiducial states[J]. THEORETICAL AND MATHEMATICAL PHYSICS,2022,213(3):1747-1761.
APA	Feng, Lingxuan,&Luo, Shunlong.(2022).From stabilizer states to SIC-POVM fiducial states.THEORETICAL AND MATHEMATICAL PHYSICS,213(3),1747-1761.
MLA	Feng, Lingxuan,et al."From stabilizer states to SIC-POVM fiducial states".THEORETICAL AND MATHEMATICAL PHYSICS 213.3(2022):1747-1761.