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

arXiv:1402.6487 · Proceedings of the National Academy of Sciences

Fair sampling perspective on an apparent violation of duality

Eliot Bolduc, Jonathan Leach, Filippo M. Miatto, Gerd Leuchs, Robert W. Boyd

Published Aug 11, 2014• 17 citations
arXivHTMLPDF

Abstract

In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited" [Scully MO, Englert B-G, Walther H (1991) Nature 351:111-116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality.

DOI
10.1073/pnas.1400106111

Related papers

The duality principle in the presence of postselection

Jonathan Leach, Eliot Bolduc, Filippo M. Miatto +3 more

The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility $\mathcal V$ and predictability $\mathcal P$ within a two-alternative system, which are bound by the inequality $\mathcal V^2+ \mathcal P^2 \leq 1$. However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e.~measures that are conditional on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. Given the ability to simultaneously obtain high predictability information and high visibility interference fringes for a wide range of coupling strengths and postselected states, this work highlights the role of fair-sampling in tests of the duality principle.

arXiv:1406.4300•Jun 17, 2014•0 citations

The duality principle in the presence of postselection

Jonathan Leach, Eliot Bolduc, Filippo M. Miatto +3 more

The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility of interference fringes and predictability of paths within a two-alternative system, which are bound by the inequality . However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e. measures that are conditioned on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. This work highlights some of the subtleties that one can encounter while interpreting familiar quantities such as which-alternative information and visibility. While we concentrated on an extreme example, it is of utmost importance to realise that such subtleties might also be present in cases where the results are not obviously violating an algebraic bound, making them harder (but not any less crucial) to detect.

Scientific Reports•Jan 29, 2016•4 citations

Simultaneous Measurement of Fringe Visibility and Path Predictability of Wave-Particle Duality

Jie‐Hui Huang, Tao Peng, Luo-Jia Wang +1 more

An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young’s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters .

Chinese Physics Letters•Aug 1, 2018•0 citations

A probabilistic view of wave-particle duality for single photons

Andrea Aiello

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 between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.

arXiv:2303.15185•Quantum•Oct 11, 2023•3 citations

Wave-particle Duality In An Atom Interferometer

Stephan Dürr, T. Nonn, Gerhard Rempe

Publisher Summary Wave-particle duality means that a quantum object can exhibit either wave or particle properties, depending on the experimental situation. The wave nature gives rise to interference phenomena, whereas knowledge about the path taken by the object testifies to its particle nature. It is impossible to observe wave and particle properties simultaneously. Atom interferometry addresses fundamental aspects of the quantum theory of measurement in real experiments. This chapter discusses the loss of interference fringes in a which-way experiment need not be due to the Heisenberg's uncertainty relation. It demonstrates how interference can be restored by erasing the which-way information. The chapter investigated a new regime, where only incomplete which-way information is available. This allowed studying the continuous transition between wave and particle pictures and to test wave-particle duality in a quantitative manner. Future experimental investigations in this field focuses on the investigation of decoherence effects to study the transition between quantum and classical physics, leading to a more detailed understanding of the processes underlying the collapse of the wave function.

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•0 citations

Interference visibility and wave-particle duality in multipath interference

Tabish Qureshi

Wave-particle duality in multipath 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 multipath experiment can actually increase the visibility of interference. As a result, it was argued that in multipath interference experiments, visibility of interference and which-path information are not always complementary observables. In the present paper, an alternative wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of paths. This relation is always respected, even in the kinds of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides an alternative way of experimentally measuring coherence in a multipath interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multipath interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multipath interference.

arXiv:1905.02223•Physical Review A•Oct 8, 2019•22 citations
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited" [Scully MO, Englert B-G, Walther H (1991) Nature 351:111-116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality.
The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility V\mathcal VV and predictability P\mathcal PP within a two-alternative system, which are bound by the inequality V2+P2≤1\mathcal V^2+ \mathcal P^2 \leq 1V2+P2≤1. However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e.~measures that are conditional on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. Given the ability to simultaneously obtain high predictability information and high visibility interference fringes for a wide range of coupling strengths and postselected states, this work highlights the role of fair-sampling in tests of the duality principle.
The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility of interference fringes and predictability of paths within a two-alternative system, which are bound by the inequality . However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e. measures that are conditioned on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. This work highlights some of the subtleties that one can encounter while interpreting familiar quantities such as which-alternative information and visibility. While we concentrated on an extreme example, it is of utmost importance to realise that such subtleties might also be present in cases where the results are not obviously violating an algebraic bound, making them harder (but not any less crucial) to detect.
An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young’s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters .
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 between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.
Publisher Summary Wave-particle duality means that a quantum object can exhibit either wave or particle properties, depending on the experimental situation. The wave nature gives rise to interference phenomena, whereas knowledge about the path taken by the object testifies to its particle nature. It is impossible to observe wave and particle properties simultaneously. Atom interferometry addresses fundamental aspects of the quantum theory of measurement in real experiments. This chapter discusses the loss of interference fringes in a which-way experiment need not be due to the Heisenberg's uncertainty relation. It demonstrates how interference can be restored by erasing the which-way information. The chapter investigated a new regime, where only incomplete which-way information is available. This allowed studying the continuous transition between wave and particle pictures and to test wave-particle duality in a quantitative manner. Future experimental investigations in this field focuses on the investigation of decoherence effects to study the transition between quantum and classical physics, leading to a more detailed understanding of the processes underlying the collapse of the wave function.
Wave-particle duality in multipath 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 multipath experiment can actually increase the visibility of interference. As a result, it was argued that in multipath interference experiments, visibility of interference and which-path information are not always complementary observables. In the present paper, an alternative wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of paths. This relation is always respected, even in the kinds of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides an alternative way of experimentally measuring coherence in a multipath interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multipath interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multipath interference.