Gram Matrices of Mixed-State Ensembles

doi:10.1007/s10773-021-04908-8

	Gram Matrices of Mixed-State Ensembles
	Sun, Yuan 3; Luo, Shunlong 1,2; Lei, Xiangyun 1,2
刊名	INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
	2021-07-23
页码	14
关键词	Gram matrices Mixed-state ensembles Affinity Fidelity Coherence Quantumness
ISSN号	0020-7748
DOI	10.1007/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
出版者	SPRINGER/PLENUM PUBLISHERS
WOS记录号	WOS:000676075000002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58956]
专题	中国科学院数学与系统科学研究院
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.