Is wave–particle objectivity compatible with determinism and locality?

  • Nature Communications 5, Article number: 3997 (2014)
  • doi:10.1038/ncomms5997
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Wave–particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies, we can test experimentally the predictions of quantum theory versus HV theories and put strong restrictions on their key assumptions. Here, we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions.

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D.R.T. thanks Perimeter Institute for support and hospitality. We thank Lucas Céleri, Jim Cresser, Berge Englert, Peter Knight, Stojan Rebić, Valerio Scarani, Vlatko Vedral and Man-Hong Yung for discussions and critical comments and Alla Terno for help with visualization. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. R.I. acknowledges support from the Institute for Quantum Computing, University of Waterloo, Canada, where this work started.

Author information


  1. Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, 077125 Bucharest-Măgurele, Romania

    • Radu Ionicioiu
  2. Research Center for Spatial Information - CEOSpaceTech, University Politehnica of Bucharest, 313 Splaiul Independentei, 061071 Bucharest, Romania

    • Radu Ionicioiu
  3. Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

    • Thomas Jennewein
    •  & Robert B. Mann
  4. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

    • Thomas Jennewein
    •  & Robert B. Mann
  5. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y6

    • Robert B. Mann
  6. Department of Physics and Astronomy, Macquarie University, Sydney, New South Wales 2109, Australia

    • Daniel R. Terno


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T.J. and R.I. conceived the entanglement-controlled protocol. D.R.T. performed the hidden-variable analysis. R.I. and T.J. produced the experimental design. R.B.M. and D.R.T. analysed the experimental signatures. All authors contributed to the writing of the manuscript. D.R.T. coordinated the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Daniel R. Terno.


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