Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Experimental test of the first- and second-order duality relations for the two-photon states

Jie‐Hui Huang, Hongyu Liu, Jiangrui Gao, Muhammad Suhail Zubairy, Shi‐Yao Zhu

Published Jul 19, 2013• 8 citations
Publisher

Abstract

The first- and second-order wave-particle dualities for two-photon states are investigated in a Mach-Zehnder interferometer. These duality relations are experimentally tested through two-photon pure states and two-photon mixed states. The experimental results are in full agreement with the theoretical predictions. The optical fields exhibiting the same first-order particlelike and wavelike behaviors may carry entirely different second-order duality information, which implies that the higher-order duality relations are a useful tool for analyzing the wave-particle duality for multiphoton states.

DOI
10.1103/physreva.88.013828

Related papers

Relation between wave-particle duality and quantum uncertainty

Hongyu Liu, Jie‐Hui Huang, Jiangrui Gao +2 more

We present a study of the relation between wave-particle duality and quantum uncertainty in a two-path interferometer and derive equalities and inequalities involving the visibility (representing wave-like behavior), the predictability (representing particle-like behavior), and their variances. We experimentally demonstrate that, for a single photon in a Mach-Zehnder interferometer, these quantities are related via an equation that connects both duality and uncertainty. This relation holds for the single-photon source prepared either in a pure state or a mixed state.

Physical Review A•Feb 6, 2012•31 citations

Higher-order wave-particle duality

Jie‐Hui Huang, Sabine Wölk, Shi‐Yao Zhu +1 more

The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality ${D}^{2}+{V}^{2}\ensuremath{\le}1$, with $D$ being the path distinguishability and $V$ being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.

arXiv:1212.4255•Physical Review A•Feb 13, 2013•24 citations

Second-Order Duality of Light and its Nonclassical Complementarity

Rikizo Ikuta

A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality character-ized by an interference visibility$V$as the wave-like property and a which-path information$D$as the particle-like property has tradeoff relation$D^{2}+V^{2}\leq 1$known as complementarity [1]–[3]. There are a lot of studies about the complementary nature of photons from various viewpoints such as delayed-choice experiments, theoretical works related to the uncertainty principle, and so on. More recently, studies have expanded the concept of the wave-particle duality to higher-order interferometric scenarios, in which the input light includes two or more pho-tons [4], [5]. Despite having a long history, all previous studies have been related to phase correlation of optical states, which reason would be why the main focus in the first place is the investigation of the mysterious quantum nature of a photon, including the superposition principle.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 26, 2023•0 citations

Wave–particle duality in a Raman atom interferometer

Aiai Jia, Jun Jie Yang, Shuhua Yan +3 more

We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ − π − π /2 type of atom interferometer, we find that the visibility ( V ) and predictability ( P ) still satisfy the duality relation, P 2 + V 2 ≤ 1.

Chinese Physics B•Aug 1, 2015•1 citation

Controlling wave-particle duality with entanglement between single-photon and Bell states

Kai Wang, Daniel R. Terno, Časlav Brukner +2 more

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest $S$ into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon $C$, which is entangled with a third photon $A$. Therefore, the individual quantum state of photon $C$ is undefined, which implements the undefined settings of the MZI for photon $S$. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.

arXiv:2112.11659•Physical Review A•Nov 28, 2022•5 citations

Mach-Zehnder interferometer for a two-photon wave packet

Luiz Carlos Ryff, P. H. Souto Ribeiro

We propose an experiment that permits observation of the de Broglie two-photon wave packet behavior for a pair of photons, using a Mach-Zehnder interferometer. It is based on the use of pulsed lasers to generate pairs of photons via spontaneous parametric down-conversion and the post-selection of events. It differs from previous realizations by the use of a third time-correlated photon to engineer the state of the photons. The same technique can give us which-path information via an ``interaction-free'' experiment and can be used in other experiments on the foundations of quantum mechanics related to wave-particle duality and to nonlocality.

arXiv:quant-ph/0010016•Physical Review A•Jan 3, 2001•2 citations
The first- and second-order wave-particle dualities for two-photon states are investigated in a Mach-Zehnder interferometer. These duality relations are experimentally tested through two-photon pure states and two-photon mixed states. The experimental results are in full agreement with the theoretical predictions. The optical fields exhibiting the same first-order particlelike and wavelike behaviors may carry entirely different second-order duality information, which implies that the higher-order duality relations are a useful tool for analyzing the wave-particle duality for multiphoton states.
We present a study of the relation between wave-particle duality and quantum uncertainty in a two-path interferometer and derive equalities and inequalities involving the visibility (representing wave-like behavior), the predictability (representing particle-like behavior), and their variances. We experimentally demonstrate that, for a single photon in a Mach-Zehnder interferometer, these quantities are related via an equation that connects both duality and uncertainty. This relation holds for the single-photon source prepared either in a pure state or a mixed state.
The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality ${D}^{2}+{V}^{2}\ensuremath{\le}1$, with DDD being the path distinguishability and VVV being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality character-ized by an interference visibilityVVVas the wave-like property and a which-path informationDDDas the particle-like property has tradeoff relationD2+V2≤1D^{2}+V^{2}\leq 1D2+V2≤1known as complementarity [1]–[3]. There are a lot of studies about the complementary nature of photons from various viewpoints such as delayed-choice experiments, theoretical works related to the uncertainty principle, and so on. More recently, studies have expanded the concept of the wave-particle duality to higher-order interferometric scenarios, in which the input light includes two or more pho-tons [4], [5]. Despite having a long history, all previous studies have been related to phase correlation of optical states, which reason would be why the main focus in the first place is the investigation of the mysterious quantum nature of a photon, including the superposition principle.
Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest SSS into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon CCC, which is entangled with a third photon AAA. Therefore, the individual quantum state of photon CCC is undefined, which implements the undefined settings of the MZI for photon SSS. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.
We propose an experiment that permits observation of the de Broglie two-photon wave packet behavior for a pair of photons, using a Mach-Zehnder interferometer. It is based on the use of pulsed lasers to generate pairs of photons via spontaneous parametric down-conversion and the post-selection of events. It differs from previous realizations by the use of a third time-correlated photon to engineer the state of the photons. The same technique can give us which-path information via an ``interaction-free'' experiment and can be used in other experiments on the foundations of quantum mechanics related to wave-particle duality and to nonlocality.