Detecting Magic States via Characteristic Functions

doi:10.1007/s10773-022-05027-8

CSpace > 应用数学研究所

	Detecting Magic States via Characteristic Functions
	Dai, Hao 1; Fu, Shuangshuang 2; Luo, Shunlong3,4
	2022-02-01
发表期刊	INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
ISSN	0020-7748
卷号	61 期号:2 页码:18
摘要	Magic (non-stabilizerness) is a crucial resource for universal fault-tolerant quantum computation in the stabilizer formalism, without which the computation can be classically emulated, as demonstrated by the celebrated Gottesman-Knill theorem. Characterizations of magic, including its detection and quantification, are of interest in quantum computation and have attracted much attention. However, most quantifiers of magic are generally quite difficult to calculate even numerically, or are restricted to systems of special dimensions. The discrete Wigner formalism has been exploited to quantify magic, although it is computable, its application is limited since its formalism is quite different in odd prime power dimensions and other dimensions. In this work, we propose a quantifier of magic in terms of characteristic functions (Fourier transforms) of quantum states, and reveal its basic properties. This quantifier, apart from its nice properties, is well defined in all dimensions and is straightforward to compute. We illustrate the effectiveness of this quantifier in detecting the magic of several representative quantum states. Employing this quantifier, we show that the group covariant symmetric informationally complete (SIC) states possess the maximal magic. Finally, we compare the quantifier of magic with some existing ones including the well known sum negativity and the so called thauma, and show that they yield different orderings of magic.
关键词	Magic states Discrete Heisenberg-Weyl group Characteristic functions Discrete Wigner functions Negativity
DOI	10.1007/s10773-022-05027-8
收录类别	SCI
语种	英语
资助项目	National Key R&D Program of China[2020YFA0712700] ; National Key R&D Program of China[2019QY0702] ; National Key R&D Program of China[2017YFA0303903] ; Fundamental Research Funds for the Central Universities[FRF-TP-19-012A3] ; National Natural Science Foundation of China[11875173]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000756806400001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60075
专题	应用数学研究所
通讯作者	Luo, Shunlong
作者单位	1.Tsinghua Univ, Ctr Quantum Informat, Inst Interdisciplinary Informat Sci, Beijing 100084, Peoples R China 2.Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Dai, Hao,Fu, Shuangshuang,Luo, Shunlong. Detecting Magic States via Characteristic Functions[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,2022,61(2):18.
APA	Dai, Hao,Fu, Shuangshuang,&Luo, Shunlong.(2022).Detecting Magic States via Characteristic Functions.INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,61(2),18.
MLA	Dai, Hao,et al."Detecting Magic States via Characteristic Functions".INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 61.2(2022):18.