Quantumness of ensemble via coherence of Gram matrix

doi:10.1209/0295-5075/134/30003

CSpace > 应用数学研究所

	Quantumness of ensemble via coherence of Gram matrix
	Sun, Yuan 1; Luo, Shunlong2,3 ; Lei, Xiangyun 2,3
	2021-05-01
Source Publication	EPL
ISSN	0295-5075
Volume	134 Issue:3 Pages:7
Abstract	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
DOI	10.1209/0295-5075/134/30003
Indexed By	SCI
Language	英语
Funding Project	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 Research Area	Physics
WOS Subject	Physics, Multidisciplinary
WOS ID	WOS:000731474100003
Publisher	IOP Publishing Ltd
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/59686
Collection	应用数学研究所
Corresponding Author	Luo, Shunlong
Affiliation	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
Recommended Citation 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.

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