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For two-path interferometers, the which-path predictability $\mathcal{P}$ and the fringe visibility $\mathcal{V}$ are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several…

Quantum Physics · Physics 2011-03-15 Berthold-Georg Englert , Dagomir Kaszlikowski , Leong Chuan Kwek , Wei Hui Chee

Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path…

Quantum Physics · Physics 2018-03-14 Yuan Yuan , Zhibo Hou , Yuan-Yuan Zhao , Han-Sen Zhong , Guo-Yong Xiang , Chuan-Feng Li , Guang-Can Guo

The notion of wave-particle duality may be quantified by the inequality V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we…

Quantum Physics · Physics 2009-10-31 Peter D. D. Schwindt , Paul G. Kwiat , Berthold-Georg Englert

We present a systematic framework to quantify the interplay between coherence and wave-particle duality in generic two-path interference systems. Our analysis reveals a closed-form duality ellipse (DE) equality, that rigorously unifies…

Quantum Physics · Physics 2025-07-09 Pawan Khatiwada , Xiao-Feng Qian

Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation ${\mathcal D}^2+{\mathcal V}^2 \le 1$. Here…

Quantum Physics · Physics 2017-09-08 Tabish Qureshi , Mohd Asad Siddiqui

Classical wisdom of wave-particle duality says that it is impossible to observe simultaneously the wave and particle nature of microscopic object. Mathematically the principle requests that the interference visibility V and which-path…

Quantum Physics · Physics 2022-04-05 Fenghua Qi , Zhiyuan Wang , Weiwang Xu , Xue-Wen Chen , Zhi-Yuan Li

One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity…

Quantum Physics · Physics 2023-10-18 Andrea Aiello

The wave-particle duality, as one of the expressions of Bohr complementarity, is usually quantified by path predictability and the visibility of interference fringes. With the development of quantum resource theory, the quantitative…

Quantum Physics · Physics 2024-01-10 Y. T. Tsui , Sunho Kim

A quantum system (quanton) traverses an interferometer with $N$ equally probable paths and interacts with another quantum system (detector) that stores path information in a set of symmetric states. In this interferometric framework, we…

Quantum Physics · Physics 2026-01-21 L. F. Melo , O. Jiménez , L. Neves

Wave-particle duality as one of the expression of Bohr complementarity is a significant concept in the field of quantum mechanics. Quantitative analysis of wave-particle duality aims to establish a complementary relation between the…

Quantum Physics · Physics 2025-05-08 Zhaofang Bai , ShuanpingDu

Wave-particle duality in multi-path interference is fraught with issues despite substantial progress in recent years. It was experimentally shown that in certain specific conditions, getting path information in a multi-path experiment can…

Quantum Physics · Physics 2019-10-11 Tabish Qureshi

We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a…

Quantum Physics · Physics 2015-07-23 Manabendra Nath Bera , Tabish Qureshi , Mohd Asad Siddiqui , Arun Kumar Pati

The complementarity of single-photon's particle-like and wave-like behaviors can be described by the inequality $D^2+V^2 \leq 1$, with $D$ being the path distinguishability and $V$ being the fringe visibility. In this paper, we generalize…

Quantum Physics · Physics 2015-06-12 Jie-Hui Huang , Sabine Wölk , Shi-Yao Zhu , M. Suhail Zubairy

The wave-particle duality demonstrates a competition relation between wave and particle behavior for a particle going through an interferometer. This duality can be formulated as an inequality, which upper bounds the sum of interference…

Quantum Physics · Physics 2018-01-31 Kaifeng Bu , Lu Li , Junde Wu , Shao-Ming Fei

Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin,…

Wave-particle duality is certainly one of the most curious concepts of contemporary physics, which ascribes mutually exclusive behaviors to quantum systems that cannot be observed simultaneously. In the context of two-path interferometers,…

The wave-particle duality has been said to contain the entire mystery of quantum mechanics. Many delayed-choice experiments have been performed to further understand the wave-particle duality. Here, we reveal some flaws in the known…

General Physics · Physics 2017-11-13 Shan-Liang Liu

Wave-particle duality, an important and fundamental concept established upon pure quantum systems, is central to the complementarity principle in quantum mechanics. However, due to the environment effects or even the entanglement between…

Quantum Physics · Physics 2017-05-31 Xiangdong Zhang , Jiahao Huang , Min Zhuang , Xizhou Qin , Chaohong Lee

Wave-particle duality relations are fundamental for quantum physics. Previous experimental studies of duality relations mainly focus on the quadratic relation $D^2+V^2\leq1$, based on symmetric beam interference, while a linear form of the…

Quantum Physics · Physics 2022-09-07 Dong-Xu Chen , Yu Zhang , Jun-Long Zhao , Qi-Cheng Wu , Yu-Liang Fang , Chui-Ping Yang , Franco Nori

Wave--particle duality demonstrates the peculiar nature of quantum mechanics. In which-way experiments, depending on the measurement scheme, a particle exhibits either wave-like or particle-like properties, as summarized by Bohr's principle…

Quantum Physics · Physics 2026-04-22 Shiyu Wang , Zhiguang Yan , Clemens Gneiting , Rui Li , Franco Nori , Yasunobu Nakamura
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