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On the reality of the quantum state


Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions that contradict those of quantum theory.

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Figure 1: Physical properties.
Figure 2: The protocol.
Figure 3: The circuit.

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  1. Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935).

    Article  ADS  Google Scholar 

  2. Popper, K. R. in Quantum Theory and Reality (ed. Bunge, M.) Ch. 1 (Springer, 1967).

    Google Scholar 

  3. Ballentine, L. E. The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42, 358–381 (1970).

    ADS  MATH  Google Scholar 

  4. Peierls, R. E. Surprises in Theoretical Physics 32 (Princeton Univ. Press, 1979).

    Google Scholar 

  5. Jaynes, E. T. in Foundations of Radiation Theory and Quantum Electrodynamics (ed. Barut, A. O.) (Plenum, 1980).

    Google Scholar 

  6. Zeilinger, A. Letter. Phys. Today 52, 13–15 (February, 1999).

    Google Scholar 

  7. Caves, C. M., Fuchs, C. A. & Schack, R. Quantum probabilities as bayesian probabilities. Phys. Rev. A 65, 022305 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  8. Spekkens, R. W. Evidence for the epistemic view of quantum states: A toy theory. Phys. Rev. A 75, 032110 (2007).

    Article  ADS  Google Scholar 

  9. Jaynes, E. T. in Complexity, Entropy, and the Physics of Information (ed. Zurek, W. H.) 381 (Addison-Wesley, 1990).

    Google Scholar 

  10. Harrigan, N. & Spekkens, R. W. Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys. 40, 125–157 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  11. Caves, C. M., Fuchs, C. A. & Schack, R. Conditions for compatibility of quantum-state assignments. Phys. Rev. A 66, 062111 (2002).

    Article  ADS  Google Scholar 

  12. Gibbs, A. L. & Su, F. E. On choosing and bounding probability metrics. Int. Stat. Rev. 70, 419–435 (2002).

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Hall, M. J. W. Local deterministic model of singlet state correlations based on relaxing measurement independence. Phys. Rev. Lett. 105, 250404 (2010).

    Article  ADS  Google Scholar 

  15. Barrett, J. & Gisin, N. How much measurement independence is needed to demonstrate nonlocality? Phys. Rev. Lett. 106, 100406 (2011).

    Article  ADS  Google Scholar 

  16. Lewis, P. G., Jennings, D., Barrett, J. & Rudolph, T. The quantum state can be interpreted statistically. Preprint at (2012).

  17. Spekkens, R. W. Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A 71, 052108 (2005).

    Article  ADS  Google Scholar 

  18. Einstein, A. Letter to Schrödinger (1935). Translation from Howard, D. Einstein on locality and separability. Stud. Hist. Phil. Sci. 16, 171–201 (1985).

    Article  MathSciNet  Google Scholar 

  19. Hardy, L. Quantum ontological excess baggage. Stud. Hist. Phil. Sci. B 35, 267–276 (2004).

    MathSciNet  MATH  Google Scholar 

  20. Montina, A. Exponential complexity and ontological theories of quantum mechanics. Phys. Rev. A 77, 022104 (2008).

    Article  ADS  Google Scholar 

  21. Montina, A. State-space dimensionality in short-memory hidden-variable theories. Phys. Rev. A 83, 032107 (2011).

    Article  ADS  Google Scholar 

  22. Regev, O. & Klartag, B. Proc. 43rd Annual ACM Symp. Theory Comput., STOC’11 31–40 (ACM, 2011).

    Book  Google Scholar 

  23. Fuchs, C. A. QBism, the perimeter of quantum Bayesianism. Preprint at (2010).

Download references


We thank K. Audenaert for code, and L. Hardy, M. Leifer and R. Spekkens for discussions. All authors are supported by the Engineering and Physical Sciences Research Council.

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M.F.P. devised the initial version of the result. All authors contributed to improvements in the result and the writing of the manuscript.

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Correspondence to Matthew F. Pusey.

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The authors declare no competing financial interests.

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Pusey, M., Barrett, J. & Rudolph, T. On the reality of the quantum state. Nature Phys 8, 475–478 (2012).

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