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Research Article

Fair sampling perspective on an apparent violation of duality

Eliot Bolduc, Jonathan Leach, Filippo M. Miatto, Gerd Leuchs, and Robert W. Boyd
PNAS first published August 11, 2014; https://doi.org/10.1073/pnas.1400106111
Eliot Bolduc
aDepartment of Physics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;
bSchool of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom;
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  • For correspondence: eliot.bolduc@gmail.com
Jonathan Leach
bSchool of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom;
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Filippo M. Miatto
aDepartment of Physics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;
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Gerd Leuchs
aDepartment of Physics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;
cInstitute of Optics, Information and Photonics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany;
dMax Planck Institute for the Science of Light, 91058 Erlangen, Germany;
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Robert W. Boyd
aDepartment of Physics, University of Ottawa, Ottawa, ON, Canada K1N 6N5;
eInstitute of Optics, University of Rochester, Rochester, NY 14627; and
fSchool of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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  1. Edited by Peter J. Rossky, The University of Texas at Austin, Austin, TX, and approved July 15, 2014 (received for review January 16, 2014)

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Significance

In 2012, Menzel et al. reported on the results of a fundamental experiment raising questions regarding the simultaneous observation of wave-like and particle-like properties in a given quantum system. Whereas the general applicability of the duality principle to entangled subsystems is an open question, we bring the current understanding of the duality principle a step forward by theoretically deriving the strongest relations between the visibility of an interference pattern and the which-way information in a two-way interferometer such as Young’s double slit. This formalism successfully describes tests of duality where postselection on a subset of the interference pattern is applied. Our analysis even reconciles the surprising results of Menzel et al. with the duality principle in its standard form.

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.

  • wave-particle complementarity
  • double-slit experiment
  • decoherence

Footnotes

  • ↵1To whom correspondence should be addressed. Email: eliot.bolduc{at}gmail.com.
  • Author contributions: E.B., J.L., and R.W.B. designed research; E.B. and J.L. performed research; E.B. and F.M.M. contributed new reagents/analytic tools; E.B. analyzed data; and E.B., J.L., F.M.M., G.L., and R.W.B. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1400106111/-/DCSupplemental.

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Apparent violation of duality
Eliot Bolduc, Jonathan Leach, Filippo M. Miatto, Gerd Leuchs, Robert W. Boyd
Proceedings of the National Academy of Sciences Aug 2014, 201400106; DOI: 10.1073/pnas.1400106111

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Apparent violation of duality
Eliot Bolduc, Jonathan Leach, Filippo M. Miatto, Gerd Leuchs, Robert W. Boyd
Proceedings of the National Academy of Sciences Aug 2014, 201400106; DOI: 10.1073/pnas.1400106111
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