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

Scientific Reports

The duality principle in the presence of postselection

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

Published Jan 29, 2016• 4 citations
Publisher

Abstract

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.

DOI
10.1038/srep19944

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

Fair sampling perspective on an apparent violation of duality

Eliot Bolduc, Jonathan Leach, Filippo M. Miatto +2 more

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.

arXiv:1402.6487•Proceedings of the National Academy of Sciences•Aug 11, 2014•17 citations

Stronger Quantum Correlations with Loophole-Free Postselection

Matty J. Hoban, Dan E. Browne

One of the most striking nonclassical features of quantum mechanics is in the correlations it predicts between spatially separated measurements. In local hidden variable theories, correlations are constrained by Bell inequalities, but quantum correlations violate these. However, experimental imperfections lead to loopholes whereby LHV correlations are no longer constrained by Bell inequalities, and violations can be described by LHV theories. For example, loopholes can emerge through selective detection of events. In this Letter, we introduce a clean, operational picture of multiparty Bell tests, and show that there exists a nontrivial form of loophole-free postselection. Surprisingly, the same postselection can enhance quantum correlations, and unlock a connection between nonclassical correlations and nonclassical computation.

arXiv:1102.1438•Physical Review Letters•Sep 14, 2011•19 citations

Quantitative wave-particle duality and nonerasing quantum erasure

Peter D. D. Schwindt, Paul G. Kwiat, Berthold‐Georg Englert

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 have investigated the relation for various situations, including pure, mixed, and partially mixed input states. A quantum-eraser scheme has been realized that recovers interference fringes even when no which way information is available to erase.

arXiv:quant-ph/9908072•Physical Review A•Dec 1, 1999•160 citations

Two sites coherence and visibility

A Piradov Mikhail

Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.

arXiv:2006.06948•Jun 12, 2020•0 citations

Interference and partial which-way information: A quantitative test of duality in two-atom resonance

Yonatan Abranyos, Matthias Jakob, János A. Bergou

We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.

Physical Review A•Dec 8, 1999•8 citations
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.
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.
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.
One of the most striking nonclassical features of quantum mechanics is in the correlations it predicts between spatially separated measurements. In local hidden variable theories, correlations are constrained by Bell inequalities, but quantum correlations violate these. However, experimental imperfections lead to loopholes whereby LHV correlations are no longer constrained by Bell inequalities, and violations can be described by LHV theories. For example, loopholes can emerge through selective detection of events. In this Letter, we introduce a clean, operational picture of multiparty Bell tests, and show that there exists a nontrivial form of loophole-free postselection. Surprisingly, the same postselection can enhance quantum correlations, and unlock a connection between nonclassical correlations and nonclassical computation.
The notion of wave-particle duality may be quantified by the inequality V2+K2< 1,{V}^{2}{+K}^{2}<~1,V2+K2< 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 have investigated the relation for various situations, including pure, mixed, and partially mixed input states. A quantum-eraser scheme has been realized that recovers interference fringes even when no which way information is available to erase.
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.
We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.