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Detecting Magic States via Characteristic Functions
Dai, Hao1; Fu, Shuangshuang2; Luo, Shunlong3,4
AbstractMagic (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.
KeywordMagic states Discrete Heisenberg-Weyl group Characteristic functions Discrete Wigner functions Negativity
Indexed BySCI
Funding ProjectNational 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 Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000756806400001
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Document Type期刊论文
Corresponding AuthorLuo, Shunlong
Affiliation1.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
Recommended Citation
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.
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