中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Gram Matrices of Mixed-State Ensembles

文献类型:期刊论文

作者Sun, Yuan3; Luo, Shunlong1,2; Lei, Xiangyun1,2
刊名INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
出版日期2021-07-23
页码14
关键词Gram matrices Mixed-state ensembles Affinity Fidelity Coherence Quantumness
ISSN号0020-7748
DOI10.1007/s10773-021-04908-8
英文摘要Gram matrices arise naturally in the consideration of pair-wise overlap of a family of vectors or quantum pure states, and play an important role in synthesizing information of a family of pure states. Since a quantum ensemble in general consists of mixed states, it is desirable to extend the concept of Gram matrix to the case of mixed states. By employing two prominent notions of overlap between mixed states, i.e., quantum affinity and quantum fidelity, one can readily extend the concept of Gram matrices of pure-state ensembles to that of mixed-state ensembles. We study these two extended versions of Gram matrices and reveal their fundamental properties. It is remarkable that while Gram matrix based on quantum affinity is non-negative definite (and thus can be regarded as a quantum state in a fictious system), the one based on quantum fidelity may fail to be non-negative definite. As applications of Gram matrices of mixed-state ensembles, we introduce two quantifiers of quantumness of ensembles via coherence of the corresponding Gram matrices, investigate their properties, and illustrate them in the qubit case.
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:000676075000002
出版者SPRINGER/PLENUM PUBLISHERS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58956]  
专题应用数学研究所
通讯作者Luo, Shunlong
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China
推荐引用方式
GB/T 7714
Sun, Yuan,Luo, Shunlong,Lei, Xiangyun. Gram Matrices of Mixed-State Ensembles[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,2021:14.
APA Sun, Yuan,Luo, Shunlong,&Lei, Xiangyun.(2021).Gram Matrices of Mixed-State Ensembles.INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS,14.
MLA Sun, Yuan,et al."Gram Matrices of Mixed-State Ensembles".INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS (2021):14.

入库方式: OAI收割

来源:数学与系统科学研究院

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