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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.


  1. Bohr, N. The quantum postulate and the recent development of atomic theory. Nature 121, 580–590 (1928).

    ADS  Article  Google Scholar 

  2. Wheeler, J. A. in Mathematical Foundations of Quantum Theory (ed. Marlow, A. R.) 9–48 (Academic Press, 1978).

  3. Wheeler, J. A. & Zurek, W. H. Quantum Theory and Measurement (Princeton University Press, 1984).

  4. Alley, C. O., Jakubowicz, O. G. & Wickes, W. C. Results of the delayed-random-choice quantum mechanics experiment with light quanta. In Proceedings of the 2nd International Symposium on Foundations of Quantum Mechanics, 36 (Physical Society of Japan, 1986).

  5. Hellmuth, T., Walther, H., Zajonc, A. & Schleich, W. Delayed-choice experiments in quantum interference. Phys. Rev. A 35, 2532–2541 (1987).

    ADS  Article  Google Scholar 

  6. Baldzuhn, J., Mohler, E. & Martienssen, W. A wave–particle delayed-choice experiment with a single-photon state. Z. Phys. B 77, 347–352 (1989).

    ADS  Article  Google Scholar 

  7. Jacques, V. et al. Experimental realization of Wheeler’s delayed-choice gedanken experiment. Science 315, 966–968 (2007).

    ADS  Article  Google Scholar 

  8. Manning, A. G., Khakimov, R. I., Dall, R. G. & Truscott, A. G. Wheeler’s delayed-choice gedanken experiment with a single atom. Nat. Phys. 11, 539–542 (2015).

    Article  Google Scholar 

  9. Shadbolt, P., Mathews, J. C. F., Laing, A. & O’Brien, J. L. Testing foundations of quantum mechanics with photons. Nat. Phys. 10, 278–286 (2014).

    Article  Google Scholar 

  10. Ma, X.-S., Kofler, J. & Zeilinger, A. Delayed-choice gedanken experiments and their realizations. Rev. Mod. Phys. 88, 015005 (2016).

    ADS  Article  Google Scholar 

  11. Greenberger, D. M. & Yasin, A. Simultaneous wave and particle knowledge in a neutron interferometer. Phys. Lett. A 128, 391–394 (1988).

    ADS  Article  Google Scholar 

  12. Jaeger, G., Shimony, A. & Vaidman, L. Two interferometric complementarities. Phys. Rev. A 51, 54–67 (1995).

    ADS  Article  Google Scholar 

  13. Englert, B.-G. Fringe visibility and which-way information: an inequality. Phys. Rev. Lett. 77, 2154–2157 (1996).

    ADS  Article  Google Scholar 

  14. Ionicioiu, R. & Terno, D. R. Proposal for a quantum delayed-choice experiment. Phys. Rev. Lett. 107, 230406 (2011).

    ADS  Article  Google Scholar 

  15. Scully, M. O. & Drühl, K. Quantum eraser: a proposed photon correlation experiment concerning observation and ‘delayed choice’ in quantum mechanics. Phys. Rev. A 25, 2208–2213 (1982).

    ADS  Article  Google Scholar 

  16. Coles, P. J., Kaniewski, J. & Wehner, S. Equivalence of wave–particle duality to entropic uncertainty. Nat. Commun. 5, 5814 (2014).

    ADS  Article  Google Scholar 

  17. Rab, A. S. et al. Entanglement of photons in their dual wave-particle nature. Nat. Commun. 8, 915 (2017).

    ADS  Article  Google Scholar 

  18. Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S. & O’Brien, J. L. A quantum delayed-choice experiment. Science 338, 634–637 (2012).

    ADS  Article  Google Scholar 

  19. Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B. & Tanzilli, S. Entanglement-enabled delayed-choice experiment. Science 338, 637–640 (2012).

    ADS  Article  Google Scholar 

  20. Tang, J.-S. et al. Realization of quantum Wheeler’s delayed-choice experiment. Nat. Photon. 6, 600–604 (2012).

    ADS  Article  Google Scholar 

  21. Roy, S. S., Shukla, A. & Mahesh, T. S. NMR implementation of a quantum delayed-choice experiment. Phys. Rev. A 85, 022109 (2012).

    ADS  Article  Google Scholar 

  22. Auccaise, R. et al. Experimental analysis of the quantum complementarity principle. Phys. Rev. A 85, 032121 (2012).

    ADS  Article  Google Scholar 

  23. Xin, T., Li, H., Wang, B.-X. & Long, G.-L. Realization of an entanglement-assisted quantum delayed-choice experiment. Phys. Rev. A 92, 022126 (2015).

    ADS  Article  Google Scholar 

  24. Zheng, S.-B. et al. Quantum delayed-choice experiment with a beam splitter in a quantum superposition. Phys. Rev. Lett. 115, 260403 (2015).

    ADS  Article  Google Scholar 

  25. Liu, K. et al. A twofold quantum delayed-choice experiment in a superconducting circuit. Sci. Adv. 3, e1603159 (2017).

    ADS  Article  Google Scholar 

  26. Chaves, R., Lemos, G. B. & Pienaar, J. Causal modeling the delayed-choice experiment. Phys. Rev. Lett. 120, 190401 (2018).

    ADS  Article  Google Scholar 

  27. Polino, E. et al. Device independent certification of a quantum delayed choice experiment. Preprint at (2018).

  28. Huang, H.-L. et al. Compatibility of causal hidden-variable theories with a delayed-choice experiment. Phys. Rev. A 100, 012114 (2019).

    ADS  Article  Google Scholar 

  29. Yu, S. et al. Realization of a causal-modeled delayed-choice experiment using single photons. Phys. Rev. A 100, 012115 (2019).

    ADS  Article  Google Scholar 

  30. Ionicioiu, R., Jennewein, T., Mann, R. B. & Terno, D. R. Is wave–particle objectivity compatible with determinism and locality? Nat. Commun. 5, 3997 (2014).

    ADS  Article  Google Scholar 

  31. Zukowski, M., Zeilinger, A. & Weinfurter, H. Entangling photons radiated by independent pulsed sources. Ann. NY Acad. Sci. 755, 91–102 (1995).

    ADS  Article  Google Scholar 

  32. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Article  Google Scholar 

  33. Langford, N. K. et al. Demonstration of a simple entangling optical gate and its use in Bell-state analysis. Phys. Rev. Lett. 95, 210504 (2005).

    ADS  Article  Google Scholar 

  34. Kiesel, N., Schmid, C., Weber, U., Ursin, R. & Weinfurter, H. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005).

    ADS  Article  Google Scholar 

  35. Okamoto, R., Hofmann, H. F., Takeuchi, S. & Sasaki, K. Demonstration of an optical quantum controlled-not gate without path interference. Phys. Rev. Lett. 95, 210506 (2005).

    ADS  Article  Google Scholar 

  36. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    ADS  Article  Google Scholar 

  37. Jacques, V. et al. Delayed-choice test of quantum complementarity with interfering single photons. Phys. Rev. Lett. 100, 220402 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  38. Ma, X.-S. et al. Quantum erasure with causally disconnected choice. Proc. Natl Acad. Sci. USA 110, 1221–1226 (2013).

    ADS  Article  Google Scholar 

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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).

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