Relative entropy between quantum ensembles

doi:10.1007/s10998-009-0223-7

CSpace > 应用数学研究所

	Relative entropy between quantum ensembles
	Luo, Shunlong1 ; Li, Nan2 ; Cao, Xuelian 3
	2009-12-01
发表期刊	PERIODICA MATHEMATICA HUNGARICA
ISSN	0031-5303
卷号	59 期号:2 页码:223-237
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.
关键词	quantum relative entropy quantum ensembles von Neumann measurements coupling quantumness
DOI	10.1007/s10998-009-0223-7
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000272075500007
出版者	AKADEMIAI KIADO RT
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7311
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.