Relative entropy between quantum ensembles

doi:10.1007/s10998-009-0223-7

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	Relative entropy between quantum ensembles
	Luo, Shunlong1 ; Li, Nan2 ; Cao, Xuelian 3
刊名	PERIODICA MATHEMATICA HUNGARICA
	2009-12-01
卷号	59 期号:2 页码:223-237
关键词	quantum relative entropy quantum ensembles von Neumann measurements coupling quantumness
ISSN号	0031-5303
DOI	10.1007/s10998-009-0223-7
英文摘要	Relative entropy between two quantum states, which quantifies to what extent the quantum states can be distinguished via whatever methods allowed by quantum mechanics, is a central and fundamental quantity in quantum information theory. However, in both theoretical analysis (such as selective measurements) and practical situations (such as random experiments), one is often encountered with quantum ensembles, which are families of quantum states with certain prior probability distributions. How can we quantify the quantumness and distinguishability of quantum ensembles? In this paper, by use of a probabilistic coupling technique, we propose a notion of relative entropy between quantum ensembles, which is a natural generalization of the relative entropy between quantum states. This generalization enjoys most of the basic and important properties of the original relative entropy. As an application, we use the notion of relative entropy between quantum ensembles to define a measure for quantumness of quantum ensembles. This quantity may be useful in quantum cryptography since in certain circumstances it is desirable to encode messages in quantum ensembles which are the most quantum, thus the most sensitive to eavesdropping. By use of this measure of quantumness, we demonstrate that a set consisting of two pure states is the most quantum when the states are 45A degrees apart.
资助项目	NSFC[10771208] ; Science Fund for Creative Research Groups[10721101] ; Key Lab of Random Complex Structures and Data Science, CAS[2008DP173182]
WOS研究方向	Mathematics
语种	英语
出版者	AKADEMIAI KIADO RT
WOS记录号	WOS:000272075500007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/7310]
专题	应用数学研究所
通讯作者	Luo, Shunlong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
推荐引用方式 GB/T 7714	Luo, Shunlong,Li, Nan,Cao, Xuelian. Relative entropy between quantum ensembles[J]. PERIODICA MATHEMATICA HUNGARICA,2009,59(2):223-237.
APA	Luo, Shunlong,Li, Nan,&Cao, Xuelian.(2009).Relative entropy between quantum ensembles.PERIODICA MATHEMATICA HUNGARICA,59(2),223-237.
MLA	Luo, Shunlong,et al."Relative entropy between quantum ensembles".PERIODICA MATHEMATICA HUNGARICA 59.2(2009):223-237.