Quantifying unsharpness of measurements via uncertainty

doi:10.1103/PhysRevA.104.052227

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	Quantifying unsharpness of measurements via uncertainty
	Liu, Yizhou 3; Luo, Shunlong 1,2
刊名	PHYSICAL REVIEW A
	2021-11-29
卷号	104 期号:5 页码:10
ISSN号	2469-9926
DOI	10.1103/PhysRevA.104.052227
英文摘要	In the conventional axiomatic formalism of quantum mechanics, a physical measurement of a quantum observable is mathematically represented by the spectral decomposition of the Hermitian operator associated with the observable. This constitutes the scenario of a Luders (projective) measurement, which includes a von Neumann (rank-one projective) measurement as a special and prominent instance. In this context, the measurement is called sharp in the sense that each measurement operator is an orthogonal projection (eigenprojection of the observable). In the modern operational formalism, a measurement is represented by a positive-operator valued measure (POVM), which consists of a family of non-negative definite operators (measurement operators, effects) summing to the identity. In this scenario, a measurement is called unsharp (fuzzy) if some measurement operators are not orthogonal projections. A natural question arises as to how to quantify unsharpness of a measurement. In this work, we address this issue in terms of uncertainty. For this purpose, we study a family of observables associated with a measurement and their uncertainty. By exploiting the difference between the (total) measurement uncertainty and the observable uncertainty, we are led to some information-theoretic quantifiers of unsharpness. We reveal their basic properties and illustrate them through some important measurements. In particular, we characterize Luders measurements and equiangular POVMs as extreme measurements in terms of unsharpness.
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[61833010] ; ORIC project from TEEP
WOS研究方向	Optics ; Physics
语种	英语
出版者	AMER PHYSICAL SOC
WOS记录号	WOS:000724666100013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59643]
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.Tsinghua Univ, Dept Engn Mech, Beijing 100084, Peoples R China
推荐引用方式 GB/T 7714	Liu, Yizhou,Luo, Shunlong. Quantifying unsharpness of measurements via uncertainty[J]. PHYSICAL REVIEW A,2021,104(5):10.
APA	Liu, Yizhou,&Luo, Shunlong.(2021).Quantifying unsharpness of measurements via uncertainty.PHYSICAL REVIEW A,104(5),10.
MLA	Liu, Yizhou,et al."Quantifying unsharpness of measurements via uncertainty".PHYSICAL REVIEW A 104.5(2021):10.