Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A strong no-go theorem on the Wigner’s friend paradox

Abstract

Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner’s friend paradox. This is a thought experiment addressing the quantum measurement problem—the difficulty of reconciling the (unitary, deterministic) evolution of isolated systems and the (non-unitary, probabilistic) state update after a measurement. Here, by building on a scenario with two separated but entangled friends introduced by Brukner, we prove that if quantum evolution is controllable on the scale of an observer, then one of ‘No-Superdeterminism’, ‘Locality’ or ‘Absoluteness of Observed Events’—that every observed event exists absolutely, not relatively—must be false. We show that although the violation of Bell-type inequalities in such scenarios is not in general sufficient to demonstrate the contradiction between those three assumptions, new inequalities can be derived, in a theory-independent manner, that are violated by quantum correlations. This is demonstrated in a proof-of-principle experiment where a photon’s path is deemed an observer. We discuss how this new theorem places strictly stronger constraints on physical reality than Bell’s theorem.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Concept of the extended Wigner’s friend scenario.
Fig. 2: A specific bipartite Wigner’s friend experiment.
Fig. 3: A two-dimensional slice of the space of correlations, illustrating the correlations discussed in this work.
Fig. 4: Results for the left-hand sides of Bell and LF inequalities for different quantum states.
Fig. 5: Experimental set-up.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The numerical codes used to determine the inequalities and to choose the measurement settings are available from the corresponding authors upon reasonable request.

References

  1. Wigner, E. P. in The Scientist Speculates (ed. Good, I. J.) 284–302 (Heinemann, 1961).

  2. Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76, 1267–1305 (2005).

    ADS  Article  Google Scholar 

  3. Leggett, A. J. The quantum measurement problem. Science 307, 871–872 (2005).

    ADS  Article  Google Scholar 

  4. Everett, H. ‘Relative state’ formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–462 (1957).

    ADS  MathSciNet  Article  Google Scholar 

  5. Rovelli, C. Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996).

    MathSciNet  Article  Google Scholar 

  6. Fuchs, C. A. & Schack, R. Quantum-Bayesian coherence. Rev. Mod. Phys. 85, 1693–1715 (2013).

    ADS  Article  Google Scholar 

  7. Mermin, N. D. Physics: QBism puts the scientist back into science. Nature 507, 421–423 (2014).

    ADS  Article  Google Scholar 

  8. Bohm, D. A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. I. Phys. Rev. 85, 166–179 (1952).

    ADS  MathSciNet  Article  Google Scholar 

  9. Bohm, D. A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. II. Phys. Rev. 85, 180–193 (1952).

    ADS  MathSciNet  Article  Google Scholar 

  10. Price, H. Toy models for retrocausality. Stud. Hist. Philos. Sci. B Mod. Phys. 39, 752–761 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  11. ’t Hooft, G. The free-will postulate in quantum mechanics. Preprint at https://arxiv.org/abs/quant-ph/0701097 (2007).

  12. Bassi, A. & Ghirardi, G. Dynamical reduction models. Phys. Rep. 379, 257–426 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  13. Penrose, R. On gravity’s role in quantum state reduction. Gen. Relat. Gravit. 28, 581–600 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  14. Brukner, Č. A no-go theorem for observer-independent facts. Entropy 20, 350 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  15. Brukner, Č. in Quantum [Un]Speakables II: Half a Century of Bell’s Theorem (eds Bertlmann, R. & Zeilinger, A.) 95–117 (Springer, 2017).

  16. Frauchiger, D. & Renner, R. Quantum theory cannot consistently describe the use of itself. Nat. Commun. 9, 3711 (2018).

    ADS  Article  Google Scholar 

  17. Proietti, M. et al. Experimental test of local observer independence. Sci. Adv. 5, eaaw9832 (2019).

    ADS  Article  Google Scholar 

  18. Baumann, V. & Wolf, S. On formalisms and interpretations. Quantum 2, 99 (2018).

    Article  Google Scholar 

  19. Healey, R. Quantum theory and the limits of objectivity. Found. Phys. 48, 1568–1589 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  20. Baumann, V., Del Santo, F. & Brukner, Č. Comment on Healey’s ‘Quantum theory and the limits of objectivity’. Found. Phys. 49, 741–749 (2019).

    ADS  Article  Google Scholar 

  21. Shimony, A. in Foundations of Quantum Mechanics in the Light of New Technology (ed. Kamefuchi, S.) 225–230 (Physical Society of Japan, 1984).

  22. Kochen, S. & Specker, E. P. The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967).

    MathSciNet  MATH  Google Scholar 

  23. Liang, Y.-C., Spekkens, R. W. & Wiseman, H. M. Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity. Phys. Rep. 506, 1–39 (2011).

    ADS  MathSciNet  Article  Google Scholar 

  24. Wiseman, H. M. & Cavalcanti, E. G. in Quantum [Un]Speakables II: Half a Century of Bell’s Theorem (eds Bertlmann, R. & Zeilinger, A.) 119–142 (Springer, 2017).

  25. Cavalcanti, E. G. Classical causal models for Bell and Kochen–Specker inequality violations require fine-tuning. Phys. Rev. X 8, 021018 (2018).

    Google Scholar 

  26. Healey, R. Reply to a comment on ‘Quantum theory and the limits of objectivity’. Found. Phys. 49, 816–819 (2019).

    ADS  Article  Google Scholar 

  27. Peres, A. Unperformed experiments have no results. Am. J. Phys. 46, 745–747 (1978).

    ADS  Article  Google Scholar 

  28. Bell, J. S. On the Einstein Podolsky Rosen paradox. Physics 1, 195–200 (1964).

    MathSciNet  Article  Google Scholar 

  29. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).

    ADS  Article  Google Scholar 

  30. Giustina, M. et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015).

    ADS  Article  Google Scholar 

  31. Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    ADS  Article  Google Scholar 

  32. Shalm, L. K. et al. Strong loophole-free test of local realism. Phys. Rev. Lett. 115, 250402 (2015).

    ADS  Article  Google Scholar 

  33. Woodhead, E. Imperfections and Self Testing in Prepare-and-Measure Quantum Key Distribution. PhD thesis, Univ. libre de Bruxelles (2014).

  34. Colbeck, R. Quantum and Relativistic Protocols for Secure Multi-Party Computation. PhD thesis, Univ. of Cambridge (2006).

  35. Pironio, S. et al. Random numbers certified by Bell’s theorem. Nature 464, 1021–1024 (2010).

    ADS  Article  Google Scholar 

  36. Acín, A. & Masanes, L. Certified randomness in quantum physics. Nature 540, 213–219 (2016).

    ADS  Article  Google Scholar 

  37. Collins, D. & Gisin, N. A relevant two qubit Bell inequality inequivalent to the CHSH inequality. J. Phys. A 37, 1775–1787 (2004).

    ADS  MathSciNet  Article  Google Scholar 

  38. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    ADS  Article  Google Scholar 

  39. Barrett, J. et al. Nonlocal correlations as an information-theoretic resource. Phys. Rev. A 71, 022101 (2005).

    ADS  Article  Google Scholar 

  40. Bong, K.-W. et al. Testing the reality of Wigner’s friend’s experience. Proc. SPIE 11200, 112001C (2019).

    Google Scholar 

  41. Lörwald, S. & Reinelt, G. PANDA: a software for polyhedral transformations. EURO J. Comput. Optim. 3, 297–308 (2015).

    MathSciNet  Article  Google Scholar 

  42. Altepeter, J. B., Jeffrey, E. R. & Kwiat, P. G. Phase-compensated ultra-bright source of entangled photons. Opt. Express 13, 8951–8959 (2005).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Australian Research Council (ARC) Centre of Excellence CE170100012, the Ministry of Science and Technology, Taiwan (grant nos. 107-2112-M-006-005-MY2 and 107-2627-E-006-001), ARC Future Fellowship FT180100317 and grant no. FQXi-RFP-1807 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation. A.U.-A., K.-W.B. and F.G. acknowledge financial support through Australian Government Research Training Program Scholarships and N.T. acknowledges support by the Griffith University Postdoctoral Fellowship Scheme. We gratefully acknowledge A. Acín for bringing ref. 33 to our attention, and thank S. Slussarenko for useful discussions. Avatars in Figs. 1 and 2 are adapted from Eucalyp Studio, available under a Creative Commons licence (Attribution 3.0 Unported), https://creativecommons.org/licenses/by/3.0/, at https://www.iconfinder.com/iconsets/avatar-55.

Author information

Authors and Affiliations

Authors

Contributions

A.U.-A., E.G.C., Y.-C.L. and H.M.W. performed the theory work. K.-W.B., N.T., H.M.W. and G.J.P. designed the experiment, which was realized by K.-W.B., N.T., F.G. and G.J.P. All authors contributed to the preparation of the manuscript and N.T. and E.G.C. took responsibility for its final form.

Corresponding authors

Correspondence to Nora Tischler or Eric G. Cavalcanti.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary discussion, Fig. 1 and Table 1.

Source data

Source Data Fig. 4

Plotted data, experiment (mean and standard deviation) and theory.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bong, KW., Utreras-Alarcón, A., Ghafari, F. et al. A strong no-go theorem on the Wigner’s friend paradox. Nat. Phys. 16, 1199–1205 (2020). https://doi.org/10.1038/s41567-020-0990-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-0990-x

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing