Quantumness of ensemble via coherence of Gram matrix
文献类型：期刊论文
| 作者 | Sun, Yuan1; Luo, Shunlong2,3 ; Lei, Xiangyun2,3
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| 刊名 | EPL
 |
| 出版日期 | 2021-05-01 |
| 卷号 | 134期号:3页码:7 |
| ISSN号 | 0295-5075 |
| DOI | 10.1209/0295-5075/134/30003 |
| 英文摘要 | The Gram matrix of a set of vectors, which encapsulates the relations between the constituent vectors, plays an important role in the exploration of both geometric and information-theoretic aspects of quantum state space. In view of its usefulness and importance, we study the Gram matrix of an ensemble of pure states (a set of pure states with a prior probability distribution) and reveal its fundamental properties. We highlight and exploit the fact that the Gram matrix of an ensemble can be formally regarded as a bona fide quantum state. The key idea is to employ coherence (with respect to the computational basis) of the Gram matrix (regarded as a quantum state) to quantify quantumness of the corresponding ensemble. In particular, we propose to use the l(1)-norm of coherence and the relative entropy of coherence, of the Gram matrix, as two significant quantifiers of quantumness. We illustrate the effectiveness and power of these quantifiers of quantumness by evaluating them for several important ensembles arising from quantum measurement and quantum cryptography. We further compare the quantumness based on the Gram matrix with various other quantifiers of quantumness in the literature, and show that although they are closely related in general, they have subtle differences and capture different aspects of ensembles, which shed light on the complexity of quantum ensembles. Copyright (C) 2021 EPLA |
| 资助项目 | National Key R&D Program of China[2020YFA0712700] ; National Natural Science Foundation of China[11875317] ; National Natural Science Foundation of China[12005104] ; National Natural Science Foundation of China[61833010] ; Natural Science Foundation of the Jiangsu Higher Education Institutions of China[20KJB140028] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000731474100003 |
| 出版者 | IOP Publishing Ltd |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59685]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Luo, Shunlong |
| 作者单位 | 1.Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Sun, Yuan,Luo, Shunlong,Lei, Xiangyun. Quantumness of ensemble via coherence of Gram matrix[J]. EPL,2021,134(3):7. |
| APA | Sun, Yuan,Luo, Shunlong,&Lei, Xiangyun.(2021).Quantumness of ensemble via coherence of Gram matrix.EPL,134(3),7. |
| MLA | Sun, Yuan,et al."Quantumness of ensemble via coherence of Gram matrix".EPL 134.3(2021):7. |
入库方式： OAI收割
来源：数学与系统科学研究院
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