Coherence as uncertainty

doi:10.1103/PhysRevA.103.042423

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	Coherence as uncertainty
	Sun, Yuan 1; Luo, Shunlong2,3
	2021-04-23
发表期刊	PHYSICAL REVIEW A
ISSN	2469-9926
卷号	103 期号:4 页码:9
摘要	Coherence of a quantum state (with respect to a fixed incoherent basis) is usually quantified by distancelike quantities, among which a particularly convenient and intuitive quantifier of coherence is based on the Hilbert-Schmidt distance between the quantum state and its dephased counterpart. This quantifier has a simple structure and many nice properties, although it is not a coherence monotone in the conventional resource-theoretic framework of coherence. Here we reveal its information-theoretic significance by showing that it coincides with uncertainty, as quantified by the variance of the state in the incoherent basis. The key point here is to regard the state as an observable, and to regard the incoherent basis as an ensemble of states rather than as measurement operators. Our result provides a natural decomposition of coherence into components along the incoherent basis. Furthermore, in terms of the Tsallis 2-entropy, which is also a measure of uncertainty, we provide two alternative interpretations of coherence: as increase of uncertainty caused by decoherence and as the conditional Tsallis 2-entropy in the context of purification. An intrinsic relation between the maximal coherence and the Brukner-Zeilinger invariant information is also established. These identifications of coherence with increase of uncertainty lead us to interpret coherence as a manifestation of quantum uncertainty, which may have implications for both quantum foundations and applications.
DOI	10.1103/PhysRevA.103.042423
收录类别	SCI
语种	英语
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	Optics ; Physics
WOS类目	Optics ; Physics, Atomic, Molecular & Chemical
WOS记录号	WOS:000646161200004
出版者	AMER PHYSICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58663
专题	应用数学研究所
通讯作者	Luo, Shunlong
作者单位	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
推荐引用方式 GB/T 7714	Sun, Yuan,Luo, Shunlong. Coherence as uncertainty[J]. PHYSICAL REVIEW A,2021,103(4):9.
APA	Sun, Yuan,&Luo, Shunlong.(2021).Coherence as uncertainty.PHYSICAL REVIEW A,103(4),9.
MLA	Sun, Yuan,et al."Coherence as uncertainty".PHYSICAL REVIEW A 103.4(2021):9.