From wave-particle duality to wave-particle-mixedness triality:an uncertainty approach  

作　　者：Shuangshuang Fu Shunlong Luo 

机构地区：[1]School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Communications in Theoretical Physics》2022年第3期27-35,共9页理论物理通讯（英文版）

基　　金：supported by the National Key R&D Program of China,Grant No.2020YFA0712700;the Fundamental Research Funds for the Central Universities,Grant No.FRFTP-19-012A3;the National Natural Science Foundation of China,Grant Nos.11875317 and 61833010。

摘　　要：The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have been proposed from an operational perspective,most of them are in forms of inequalities,and some of them are expressed in forms of equalities by incorporating entanglement or coherence.In this work,we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer,with uncertainty as a unified theme.More specifically,by employing the simple yet fundamental concept of variance,we establish a resolution of unity,which can be interpreted as a complementarity relation among wave feature,particle feature,and mixedness of a quantum state.This refines or reinterprets some conventional approaches to wave-particle duality,and highlights informational aspects of the issue.The key idea of our approach lies in that a quantum state,as a Hermitian operator,can also be naturally regarded as an observable,with measurement uncertainty(in a state)and state uncertainty(in a measurement)being exploited to quantify particle feature and wave feature of a quantum state,respectively.These two kinds of uncertainties,although both are defined via variance,have fundamentally different properties and capture different features of a state.Together with the mixedness,which is a kind of uncertainty intrinsic to a quantum state,they add up to unity,and thus lead to a characterization of the waveparticle-mixedness complementarity.This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.

关 键 词：wave-particle duality complementarity mixedness UNCERTAINTY TRIALITY 

分 类 号：O413[理学—理论物理]