KMS Of Academy of mathematics and systems sciences, CAS
| Detecting Magic States via Characteristic Functions | |
Dai, Hao1; Fu, Shuangshuang2; Luo, Shunlong3,4
| |
| 2022-02-01 | |
| Source Publication | INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
 |
| ISSN | 0020-7748 |
| Volume | 61Issue:2Pages:18 |
| Abstract | 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. |
| Keyword | Magic states Discrete Heisenberg-Weyl group Characteristic functions Discrete Wigner functions Negativity |
| DOI | 10.1007/s10773-022-05027-8 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Physics |
| WOS Subject | Physics, Multidisciplinary |
| WOS ID | WOS:000756806400001 |
| Publisher | SPRINGER/PLENUM PUBLISHERS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60075 |
| Collection | 应用数学研究所 |
| Corresponding Author | Luo, Shunlong |
| Affiliation | 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 |
| 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment