Quantum wave–particle superposition in a delayed-choice experiment

An Author Correction to this article was published on 28 April 2020

This article has been updated


Wave–particle duality epitomizes the counterintuitive character of quantum physics. A striking illustration is the quantum delayed-choice experiment, which is based on Wheeler’s classic delayed-choice gedanken experiment, but with the addition of a quantum-controlled device enabling wave-to-particle transitions. Here, we realize a quantum delayed-choice experiment in which we control the wave and the particle states of photons and particularly the phase between them, thus directly establishing the created quantum nature of the wave–particle. We generate three-photon entangled states and inject one photon into a Mach–Zehnder interferometer embedded in a 186-m-long two-photon Hong–Ou–Mandel interferometer. The third photon is sent 141 m away from the interferometers and remotely prepares a two-photon quantum gate according to independent active choices under Einstein locality conditions. We realize transitions between wave and particle states in both classical and quantum scenarios, and therefore tests of the complementarity principle that go fundamentally beyond earlier implementations.

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Fig. 1: The evolution of delayed-choice experiments.
Fig. 2: Experimental configuration.
Fig. 3: Continuous transitions between particle and wave states in both classical and quantum scenarios.
Fig. 4: Witnessing the wave–particle quantum superpositions.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 28 April 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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We thank J. Kofler and Č. Brukner for helpful discussions, and M. Chen for taking the birds-eye-view photograph of the experiment. This research is supported by the National Key Research and Development Program of China (2017YFA0303700), the National Natural Science Foundation of China (grants nos. 11690032, 11674170 and 11621091), the National Science Foundation of Jiangsu Province (no. BK20170010), the programme for Innovative Talents and Entrepreneur in Jiangsu and the Fundamental Research Funds for the Central Universities.

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K.W., Q.X. and X.-s.M. designed and performed the experiment. K.W. and X.-s.M. analysed the data. K.W. and X.-s.M. wrote the manuscript with input from all authors. S.Z. and X.-s.M. supervised the project.

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Correspondence to Xiao-song Ma.

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Wang, K., Xu, Q., Zhu, S. et al. Quantum wave–particle superposition in a delayed-choice experiment. Nat. Photonics 13, 872–877 (2019). https://doi.org/10.1038/s41566-019-0509-0

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